Kitty Pryde (of many names, notably Shadowcat) was introduced to the 
team in UXM #129, just as the Hellfire Club intrigue and the Dark 
Phoenix Saga were getting underway. The Phoenix Saga left Jean Grey 
dead on the moon in UXM #137, which led to Cyclops' departure in #138 
and Kitty (first called Sprite and Ariel) joining in #139. Cyclops 
returned just in time to join the team in space for the Brood Saga, 
UXM #161-167.

Around UXM #160, Claremont and then-editor Louise Jones (who was yet to 
marry Walt Simonson), concieved a new title that would focus on the 
school aspect of the X-Men, instead of the superheroics. Apparently 
someone in Marvel had decided that there should be a companion book to 
the X-Men, and Claremont was anxious to avoid what he called a "West 
Coast X-Men" book.

This spinoff book had no title for a long time, until the creators 
decided to use the term which they had just been using in their design 
meetings for it: the New Mutants. This was also a tribute to the 
Kirby/Lee X-Men, since the original name for that comic was going to be 
"The Mutants," until someone convinced Stan Lee that not enough of the 
buying public knew what mutants were to make it a sensible title. 
Claremont was the writer of the New Mutants, and Bob McLeod was the 
first penciler. The New Mutants debuted with Sunspot (Roberto DaCosta), 
Wolfsbane (Rahne Sinclair), Psyche (Dani Moonstar), Karma (Xi'an Coy 
Manh), and Cannonball (Sam Guthrie). They fought Donald Pierce, a 
renegade member of the Hellfire Club, in their first appearance. Over 
the years, they were joined by Magma (Amara Aquilla), Magik (Illyana 
Rasputin, Colossus' sister), Cypher (Doug Ramsey), and Warlock (an 
alien being, not to be confused with the cosmic superhero of the same 
name). The title was cancelled and rebooted after issue #100.

Kitty Pryde was demoted to the New Mutants for a short while, but soon
rejoined the X-Men team as Shadowcat. Rogue joined the team in UXM #171,
and Phoenix II (Rachel Summers, daughter of an alternate Jean Grey) was
introduced in the late 180s of the title. Meanwhile, former X-Men team
members Angel, Beast, and Iceman all resurfaced in "The Defenders", 
retitled "The New Defenders", for a couple of years. Cyclops, on his own
leave of absence, met and married Madelyne Pryor, who looked like Jean. 
Together, they had a son, Nathan Christopher Charles Summers, who was 
born in UXM #200 while the New Mutants and X-Men were in Asgard.

Around the time of UXM #200, a third team/title was introduced.  These
would be mutants disguising themselves as humans to help fight mutant 
hatred. Bob Layton was the writer and Jackson Guice was the penciler, 
and the title was called X-Factor, after the genetic trait that the X-
Factor members would be hunting down. Heavily promoted in the Marvel 
trade press, the original X-Factor consisted of Cyclops, Iceman, the 
Beast, Angel, and Jean Grey. Marvel attempted suspense by keeping the 
mysterious "fifth member" unrevealed, but since the four men were known 
going in, it was obvious that they were going to resurrect Jean Grey for 
the title. X-Factor found themselves bringing in Rusty Collins, a 
pyrokinetic, in their first appearance. They, too, trained young 
mutants, bringing in Tabitha Smith (of many codenames including 
Meltdown) and others.

Soon after that, Chris Claremont came up with an idea that would prove 
to be the bane of straightforward storytelling in the X-Titles: a 
crossover. While crossovers were used in comics at that time (especially 
at Marvel--see Secret Wars II), a multi-title crossover on the scale of 
the Mutant Massacre (a title used in partial irony) was pretty new. In 
it, X-Men Nightcrawler, Colossus, and Shadowcat were badly hurt, while 
X-Factor member Angel lost his wings. Psylocke (Betsy Braddock), Dazzler 
(Alison Blaire), Longshot, and Havok joined the X-Men in the following 
months.

The Mutant Massacre crossover was so popular that the editor of the X-
Men, Ann Nocenti, decided to hold another one to help keep sales up 
during the competitive summer months. Claremont agreed, and presented 
the Fall of the Mutants--unique in that while it was a "crossover," none 
of the characters of one book met the characters of the other two books. 
However, the result was tons of bloodshed--Angel became Archangel, Doug 
Ramsey was killed, and the team of X-Men, plus Madelyne Pryor, was 
killed. Of course, Madelyne and the X-Men were resurrected, but were 
invisible to scanners. They went to Australia and were joined by silent 
teleporter Gateway.

With the interest in the X-titles remaining at a high level, Classic X-
Men was created to reprint the adventures of the "new" X-Men, beginning 
with Giant-Size X-Men #1. Unlike most reprint books, Classic X-Men also 
had up to four new pages inserted into the old story, sometimes not with 
the most smooth of seams, written by Claremont and drawn by some current 
artist, which would expand upon the old story. Each Classic X-Men also 
had a brand new story that took place around the time of the reprint. 
The first run of new stories in Classic X-Men were written by Claremont 
and drawn by John Bolton. When the press of Claremont's writing didn't 
give him time to write any more in Classic X-Men, a few other writers 
were allowed to do some, but eventually Marvel removed the backup 
stories (last backup: #44, the Rogue origin story) and the new "filler" 
material, and retitled the book X-Men Classics, which reprinted 
unaltered copies of Uncanny X-Men. This title was cancelled at #110 
(which reprinted UXM #206).

For a long time, Chris Claremont opposed giving Wolverine a solo title. 
Claremont feared that overexposure would ruin the mysterious nature of 
his background which helped make him so popular (Marvel solved that 
dilemma by making Wolverine's revealed past so confusing that nobody 
could figure it out). A few Wolverine limited series came out, such as 
"Wolverine" and "Kitty Pryde and Wolverine", but neither fulfilled the 
thirst for more Wolverine stories. Wolverine finally got an ongoing 
series, previewed in the new weekly comic, Marvel Comics Presents. In an 
attempt to cut down the "fanboy" appeal, which Claremont feared was 
driving requests for the title and would ruin its long-term prospects, 
he deliberately set the popular mutant in an unpopular setting for young 
fans--the exotic South Seas of Madripoor. Based more on old movies than 
pop comics, Madripoor was both an attempt by Claremont to write the 
character in a setting he found fun, as well as to confound the fanboys 
who were just looking for "cool" action scenes. By putting Wolverine 
into yet another personality, as "Patch," Claremont also could keep 
mystery up around the mutant without revealing his ever-appealing "true 
background."

By this time, X-Factor's hidden agenda of pretending to be mutant 
hunters while actually saving mutants had been exposed. They were living 
as just another mutant superhero team in Ship off the coast of New York. 
At the same time, some of the X-Men who were separated during the Mutant 
Massacre and Fall of the Mutants had moved to England and set themselves 
up (with some established English heroes) as Excalibur. Chris Claremont 
wrote and Alan Davis pencilled the book. The first members were Captain 
Britain (Brian Braddock), Nightcrawler, Shadowcat, her dragon Lockheed, 
Meggan, and Phoenix II, and they were challenged by Mojo's Warwolves in 
their first appearance. The book was cancelled with #125.

Around this time, Claremont planned to do one last crossover that would 
clear up a bunch of loose ends, finalize some old plot threads, get rid 
of some old characters, and answer some old questions. It was called 
Inferno, and was distinctive for how non-mutant titles worked themselves 
into the story without being required reading (like Spider-Man's 
appearances in Inferno). Basically, two demons teamed up with Madelyne 
Pryor (who was revealed to be Sinister's clone of Jean Grey and called 
herself the Goblyn Queen), and gathered babies for a sacrifice that 
would allow them to take over the world. Scott and Maddie's son was one 
of the babies. The X-Factor kids and the New Mutants teamed up to rescue 
the babies, while X-Men and X-Factor met, saw the real true Jean Grey 
was alive, and trounced Sinister. 

Claremont hoped that Inferno would be so unwieldly that no one would 
want another crossover. It didn't work. Inferno just made people want 
more "X-overs". This meant more writers had to be called in, and it
increased the chance that artists and writers would mess up continuity 
and otherwise have their quality of work suffer. Despite the fact that 
crossovers end up producing lower quality work from all involved in the 
stories, poorly-planned and ill-plotted crossovers continued for years.

After the events of Inferno, the team was "joined" by mall rat Jubilee 
(Jubilation Lee). During various events, most of the team ended up going 
through the Siege Perilous, which sent characters all over the world and 
"resurrected" them in new situations (such as Havok as a military leader 
in Genosha, Colossus as an artist in New York, Rogue split from the 
Carol Danvers persona in the Savage Land, and Psylocke as an Asian 
ninja). Poor Storm had been deaged by Nanny and thought dead, though she 
ended up as a child thief with Gambit (Remy LeBeau) in New Orleans. A 
short-term team of backup X-Men was formed on Muir Island with Legion, 
Forge, Siryn, Banshee, and a few others. They went looking for the other 
X-Men.

Shortly after this, Claremont was getting burned out on the X-titles. He
was writing most of the issues while working on novels, and he started 
to fold under pressure from editorial influences as to what should be in 
the X-titles (as well as his own recycling of old ideas). Wolverine and 
New Mutants were the first books he resigned from. Wolverine was moved 
to a variety of writers, eventually settling on Larry Hama for a long 
stretch, while New Mutants was passed on to Louise Simonson. 

Somewhere around here Rob Liefeld stepped in. He was brought over to New 
Mutants because Marvel thought a young penciler might better relate to 
young characters. Bob Harras, the editor of the X-titles (note that the 
titles had grown large enough that a group editor was needed to keep 
them all together) thought the title of "New Mutants" was oxymoronic on 
a book approaching its one hundredth issue, and wanted a change in the 
focus of the book to match the change of title. So, he put Rob Liefeld 
on New Mutants as penciler, with Louise Simonson as writer. Cable was 
introduced as their mysterious leader. Half of the team left. The 
remainder was kidnapped by former X-Factor assistant Cameron Hodge and 
taken to Genosha where they were put on trial. 

This led to the X-Tinction Agenda, where all of the various characters 
of X-Factor, X-Men, and New Mutants reconnected. Warlock was killed, the 
kids were rescued, and everyone tried to figure out how they should 
proceed. The New Mutants and X-Factor kids stayed with Cable (except 
Wolfsbane), while the others contacted Xavier in space (where he'd been 
since UXM #200). They soon fought the Shadow King, and again tried to 
figure out what to do. So, around UXM #281 and X-Factor #71, there was a 
massive reshuffling of teams.