History of the Doom Patrol Part 3: Volume 2

Pre-Grant Morrison

Scott (left), Karma, Celsius, Lodesone, Tempest, Larry (not member) Negative Women and Robot Man

The series was relaunched after the time-altering event Crisis on Infinite Earths. The Doom Patrol's history was largely intact. However, the original members didn't die, but were not active heroes. In his version, the writer changed hands several times.
This version had all of the members of the previous one, but also introduced new members. Introduced new members were Lodestone, Karma and Scott Fischer. Lodestone and Karma didn't actually care about being superheroes and joined the team for other reasons. Because Grant Morrison was going to take over, the writer, Paul Kupperberg, got rid of the Patrol members Grant didn't want: Scott Fischer was killed the gene-bomb from Invasion, Celsius was killed by an explosion during the same event, Karma continue to run away from the law, the Negative Spirit left its host, Lodestone was comatosed and Tempest became the physician of the team. He also established future members Dorothy Spinner, Danny the Street and Crazy Jane. Members of this version include:

• Lodestone / Rhea Joanes- She had the ability to control the electromagnetic spectrum and enhanced her physical abilities. She got these power from an electromagnetic blast. She joined for a sense of security. She was comatose by end of the run.
• Scott Fischer- He was the only new member that actually wanted be a hero. He tended to be naive. His hands generated a burning aura that forced him to wear gloves. He was the only person killed by the gene-bomb. 
• Karma / Wayne Hawkins- He could generate bad luck. He was forced to leave when he was hunted by the law for crimes he committed. He later joined the Suicide Squad.
• Celsius / Arani Desai
• Negative Woman / Valentina Vostok
• Robotman / Cliff Steele
• Tempest / Joshua

Grant Morrison

Clockwise: Rebis (top), the Chief, Crazy Jane, Robotman and Dorothy Spinner

Grant Morrison took over the series. Whereas other writers focused more on the superhero ascept of the comic, Grant Morrison decided to focus on the strange and weird tone. As such, he incorporated surrealism, elements of dadaism, cut-up techniques and influences from Jorge Luis Borge, William S. Burrought, Heinrich Hoffmann and Brion Gysin. He also parodied and homaged Swamp Thing: A Murder of Crows (in issue 31 and 32), Charles Atlas (via the character Flex Mentallo, who was originally supposed to be the actual character), the Jack Kirby and Stan Lee-era Fantastic Four (in issue 53), X-Force (in an one-shot comic Doom Force) and the Punisher (see below).
Niles assembled a new Doom Patrol to combat the villainous Scissorsmen. This team fought villains that were even odd for this series such as the godlike being Red Jack (who needed pain to survive), a Punisher-parody Beard Hunter (who kills people with facial hair) and the reason and order-hating Brotherhood of Dada. In the last storyline, it turned out the Chief caused the accidents that created the original Doom Patrol and (after murdering Tempest) unleashed nanobots to cause a catastrophe to make the world even weirder. However, the Candlemaker, one of Dorothy's creations, decapitated him. Members of this version included:

• Rebis- Larry's Negative Spirit turned out to be alive and combined Larry and a Tempest's wife into a new body. Rebis was the resulting creation. Rebis was a hermaphrodite that has Larry's powers, flight and powers that appear on and off.
• The Chief- He was leader. Unlike the original version of the character, he was portrayed as cold and detached. He is later revealed to be evil and was decapitated by one of Doroth's creaions.
• Crazy Jane- She suffered from multiple personality disorder. Due to being exposed to the gene-bomb, each of her personalities has a different set of powers.
• Robotman / Cliff Steele- He has rejoined the team. He gained a new body at one point, but lost it and was forced to reuse his old one.
• Dorothy Spinner- She is a little girl that had a deformed face. She was emotionally vulnerable. She has the ability make her imaginary beings real. However, they gain independent thought upon being created. 
• Danny the Street- He was a living street named after Danny La Rue ("La Rue" is French for "The Street"). 
• Tempest / Joshua- While he still had his powers, he was now the team physician.

Post-Grant Morrison

I couldn't find a group shot.

Grant Morrison left of the series with the sixty third issue. As such, Rachel Pollack became the writer. Dorothy Spinner became a more prominent member. The run had themes of bisexuality, transgenderism, identity, humanity and the generation gap.
The Chief was frozen. Realizing what he did, the Chief (who kept himself alive via nanonites) wanted to atone for his sins. He, Dorothy Spinner and Robotman formed the new Doom Patrol. Their base was the haunted house Violet Valley's Rainbow Estates. Three new members joined: George and Marion / the Bandage People (ex-members of the Builders, who are similar to the Men from N.O.W.H.E.R.E.) and Inner Child. Kate Godwin / Coagula later joined thus becoming one of the few transgender superheroes.
Their villains included the animal spirits Fox and Crow (who hated Dorothy), the weirdness-hating government agents Builders, the fetus-in-a-bubble Master Cleaner (who "cleans" the world by replacing everything with stolen items) and Rabbi of Darkness and his False Healers (a team of Hassidic healers). Cliff's brain was becoming completely robotic but Dorothy's imaginary friends "repaired" him. The Chief died trying while trying to enter the Tree of Life / Sephirot. Members were:

• The Bandage People- Marion and George were members of Builders. Their bodies were stolen and their minds were transfered to bodies made out of bandages. They could manipulate and extend their bandages. 
• Coagula / Kate Godwin- Having slept with Rebis, she gained the ability to coagulate liquids and disslove solids by touching these sustances. She is most notable for being one of the few transgender superheroes. She was originally the male Clark Godwin. 
• The Chief- His head was frozen in order to preserve it. Nanobots altered his head so he could survive without a body. He decided to become a Doom Patrol member to atone for his sin.
• Dorothy Spinner- She was now a more prominent member. She would use her "imaginary" friends to help the team during combat.
• Inner Child- It was a manifestion of the innocence and purity of the ghosts in the Rainbow Estate.
• Robotman

References:
http://en.wikipedia.org/wiki/Doom_Patrol
http://dc.wikia.com/wiki/Rhea_Jones_(New_Earth)
http://dc.wikia.com/wiki/Scott_Fischer_(New_Earth)
Doom Patrol: Crawling From the Wreckage
http://en.wikipedia.org/wiki/List_of_Doom_Patrol_members
http://villains.wikia.com/wiki/Beard_Hunter
http://dc.wikia.com/wiki/Dorothy_Spinner_(New_Earth)
http://en.wikipedia.org/wiki/Danny_the_Street
http://www.comicvine.com/bandage-people/4060-57107/