The original Batman disappeared in the mid-60s, his place taken by his former companion, Robin, who adopted the circle-around-the-bat motif. That Batman brought in a new, female, aide called Huntress in 1977. The second Batman was killed by a cabal of his enemies in 1984 and the Huntress continues the Batman tradition to this day. Huntress now has a partner named Nightwing who is being trained to eventually take her place.
That Huntress is really Helena Wayne, the daughter of Bruce Wayne (Batman I), and Nightwing is really Bruce Grayson, son of Richard Grayson (Robin I/Batman II) is known only to a few of their intimate acquaintances and colleagues.
Since the death of the second "legitimate" Batman, there have been several attempts by others to take up the name, including one villain who had a short career in the Squadron Sinister before being beaten within an inch of his life by Power Woman. Most of the "Batmen" have been exemplary in one facet of the original's abilities. There has been an excellent martial artist, a clever detective, and an ingenious gadgeteer. There was even one putative successor who built his crimefighting around a series of vehicles. All have retired from crimefighting very shortly after their debuts, often after a villain (frequently the Joker or Harly Quinn) has exploited their lack of expertise in a field their skill sets didn't cover.
All of these aspiring Batmen have come under the scrutiny of Huntress, who has not been impressed.
Probably the most interesting aspirant in recent time has been the villain known as Foxbat. In 2002, he appeared in Houston and began fighting crime as Batman. Sources indicate that one reason for this impersonation was his attempt to impress the ISIS member called Radiance, whom he had earlier courted as himself. Foxbat-Batman actually had some successes, mostly working with the ISIS team, and only stopped the masquerade after a personal visit from Huntress and Nightwing. Observers have suggested that Foxbat had the success he did because he was able to submerge his own personality into an overblown version of the Darknight Detective's public persona.