How they started out

The Family started out with just Alfred and Commissioner James Gordon. The family began to grow when Dick Grayson the first Robin became Batman's partner.

Then about two years later Barbara Gordon became the first Batgirl. Batman was at first reluctant to let Barbara become Batgirl but she later convinced him to train her. The trainings paid off and she was able to defeat a group of bank robbers.Though when she was paralysed she was still part of the Batman family and became Oracle, a information broker for heroes.

As Dick became older he adopted a new costume and name: Nightwing, but still came to the aid of Batman when he was needed. He has since been almost married twice and is currently part of a Titans team.

As Batman always needed a Robin, Jason Todd came in, sadly until recently he was killed by Joker, since his return he was become estranged from the Batman family.

Sometime in between Huntress (Helena Bertinelli) was introduced as a rather brutal and reckless vigilante. Most of the time Batman didn't approve of her methods which normally includes giving them a brutal beating, but since then she has partially curbed this. At one part she was kicked out of the family when she was accused of murder but was found innocent.Since then she has been welcomed into the family.

Then later came Tim Drake, the third Robin after a number of tests so he wouldn't end up like Jason Todd, he was accepted into the Batman family. He has also become a character in him own right heading a team of Teen Titans.

In Batman: Knightfall, Batman had his back broken by Bane. To replace him he asked not Nightwing but Azrael, but he was later replaced by Nightwing when Azrael became unstable. Azrael later died.

Cassandra Cain is Batgirl she is the daughter of the assassin David Cain and Lady Shiva. She was first introduced in No Man's land and later took the Batgirl mantle when she protected James Gordon from her own father, David Cain. She was then trained with Barbara, who approved of Cassandra, who she though of as a daughter. For a time she became estranged from the family but recently it is thought to have made a come back into Bat's " good books" since joining the Outsiders.

After Time came another ally, Spoiler who was also the daughter of the villain Cluemaster.Sadly she is now deceased. (Or so we think) She also served as the first female Robin in Tim's place for a few days. Also not soon after came Orpheus who's current status or even if he is alive is unknown.

With the storyline Hush, the Bat family welcomed Catwoman to the group. But her status with the family is unknown since she had a daughter.

Most recently of all though has been the introduction of a new Batwoman: Kate Kane. She is highly noted in the Batman family as she is a lesbian.

Renee Montoya who is the Question and a former member of Gotham City Police Department, she has who has close ties with Batwoman. She is also a lesbian.

One extended family members is Black Canary, who was featured in the Batman Family storyline but said herself that she is not in close friendship with Batman.

Alternate Timelines and Pre Crisis.

Pre-Crisis

Pre Crisis was the introduction of the fist Bat-Woman and Bat-girl : Kathy Kane and Betty Kane. It also brought Bat-mite ( Who recently also returned), Ace the Bat Hound and Helena Wayne. All these characters except Bat-mite were wiped out during Crisis on Infinite Earths, Though Helena Wayne may be brought back since the Multiverse returned in 52.

Alternate Timelines and Elseworlds.

In Elseworlds : Dynasty, Brenna Wayne, a descendent of Bruce Wayne has taken up the role as Batwoman to fight Vandal Savage.

In Superman/Batman, Helena Bertinelli instead of becoming Huntress she has become Batwoman, donning a costume similar to the Batman himself.

In The Dark Knight Returns and Dark Knight Strikes Again Carrie Kelly becomes Catgirl, a sidekick for Batman.

In All Star Batman and Robin, Black Canary has close ties with Batman, maybe even romantic. The storyline is ongoing.