BruDami

BruDami is the family ship between Bruce Wayne and Damian Wayne from the DC Comics fandom.

Canon
Unlike his three other Robins who became his adoptive sons, Damian is Bruce's biological son he had with Talia al Ghul, who drugged Bruce so he could grant her his child. Bruce wasn't aware of Damian's existence until Talia brought their son before him, while Talia had kept the identity of her son's father secret from him before she made the decision for the two to finally meet. Like most kids Damian wants to make his father proud of him, as well as for his parents to work things out so the three of them can be a family, but their codes and separate paths that have them as enemies kept that from happening. Along with forcing Damian to choose between the kill or none kill ways of his parents. Damian's time as Robin had him choose his father's way, even though hanging onto what Talia had drilled into him from his earlier years has it clashing with Bruce's ideals of fighting crime. Bruce on the other hand hasn't given up hope that he'll be able to help Damian fight his killing nature in order to keep it at bay. Due to the way Jason had turned out when he failed to help his second Robin tame his build up anger, he didn't want to make the same mistake with Damian. This had Bruce being a bit more harder on Damian than he was with Dick and Tim, until Damian became a little less selfish and began using his father's justice not vengeance code.

Injustice
Things between Bruce and Damian in the Injustice universe take a turn for the worse, as Damian acceptedly killing Nightwing had led to Batman disowning his bio son while morning the death of his adoptive son. Even though Dick's soul, Deadwing, as forgiven Damian for his death and allows him to become the new Nightwing in his place. Batman, however, wasn't aware that Dick had forgiven Damian and disapproved of him taking up his murdered son's alter ego. Damian's assassin upbringing had him agreeing with Superhero's ideals on peace and sides with him, while seeing him as a replacement father. Making Bruce and Damian enemies in the war between Batman and Superman. Bruce had assumed that Damian's actions were deliberate and him killing Dick was his way of getting ride of a rival, from how Damian had tried to make himself the better Robin than Dick was, hence why he began to think that reforming Damian from his killing ways was a lost cause.

Damian's ending in Injustice 2, however, had Batman sacrifice himself to save his son from a killing blow that was meant for him. This had Damian avenge his father by killing Brainiac, despite the times he had hated Bruce and wanted to escape the Batman's shadow, but after seeing the bat symbol stained with the blood he shares him his father, he became the new Batman in his father's place. The 2021 Injustice film also had Damian show concern for his father when he saw the Batman and a few other League members fight Amazo, showcasing that a part of him still cared about Bruce and had wanted to help the heroes in their battle with Amazo; what his grandfather kept than from happening.

In the Lego world of the DC universe Batman is shown to be a bit over protective of Damian, as  reveals that he was worried that his son might turn into Jason. Lego Damian being a happier version of the original Damian Wayne has him enjoying his time as Robin and fighting crime with his father. Who has worked out a bat curfew that allows Damian to continue his education, so he can gain skills to help him in the world, as well as hours he would allow Damian to accompany him on portal. Nightwing notices how Batman's worries has him pushing Damian away and does what he can to remind Bruce that Damian isn't Jason, and how pushing him away might make his fear come true. Like most kids, Damian wasn't happy with his father being too over protective of him, as well as being hard on him to the point it has Batman ordering Robin to stay within the safety of the Batcave; while Damian finds to sneak out so he can join his father and allies. Dick helps Damian to realise that Bruce being hard on him is because he cares and just wants to keep his son safe. At the end of Family Matters Batman is impressed with how Damian was able to help their bat-family allies keep the city safe and showing inactive through buildolagy, he felt that he can trust his son with other responsibilities. Like walking Ace in return for going on portal with him.

Moments
Lego DC Batman: Family Matters
 * Robin appeared stunned when he hears Batman say to Red Hood that the train station Damian was at earlier with Nightwing, was where his parents had met.

Fanon
Damian being Bruce's biological son than another ward is what draws fans to them, even though many are put off by Damian's spoiled attitude and wondering if he'll become another Jason Todd. As there had been moments when it looked like that would happen.

Fandom
TUMBLR

Trivia

 * One of the endings of the interaction movie version of Under the Red Hood, Batman: Death in the Family has Bruce being aware that Talia had became pregnant with his child, but instead of allowing Batman to become part of Damian's early years Talia tells Bruce that she had lost their child before he was born. As Bruce cutting ties with Talia after Jason was gravely hurt meant that Damian had lost a father figure, and got Talia to ask Jason to help her raise him. While being unaware that Jason plans to use Damian to destroy Bruce.

Variations

 * Batfamily refers to the ship between Bruce, Damien, Selina Kyle, Alfred Pennyworth, Dick Grayson, Jason Todd, Stephanie Brown, Tim Drake, Cassandra Cain, Lucius Fox, and the other sidekicks of Batman