The New Fantastic Four were assembled by Sue Storm (in actuality a Skrull named De'Lila) to avenge the supposed deaths of the original Fantastic Four (whom the Skrull had captured).
The New Fantastic Four were created by Walt Simonson and Arthur Adams and first appeared in Fantastic Four #347.
Although, never remaining together too long, the New Fantastic Four have reunited on occasion. The original team was intended to be entirely tongue-in-cheek by the fact that it was just a team of Marvel's then hottest characters (exemplified by one cover which also promises an appearance of the Punisher). Despite that, subsequent writers brought the New Fantastic Four back with little to no irony in their existence. During one reunion, Sleepwalker was substituted for Wolverine and in more recent appearances Dan Ketch has been replaced with Johnny Blaze since the latter re-assumed his Ghost Rider persona. The original team's most recent reunion was during Fear Itself, although a new iteration of the team formed in the pages of Venom featuring analogues to the original team whom similarly didn't remain together for long. In this case, the team consisted of: Venom (rather then Spider-Man) Red Hulk (rather then Hulk) Alejandra Jones (rather then Dan Ketch/Ghost Rider) and X-23 (rather then Wolverine).
In Ghost Rider vol. 8, another reference to the team occurs, bringing back Laura/X-23 (now going by Wolverine), and using Robbie Reyes as the Ghost Rider, Amadeus Cho as the Hulk, and Silk as the analogue to Spider-Man.