Were the historical Alexander and Hephaestion lovers?

Most likely. In Old Greece it was a matter of what role you had in a relationship; not what gender. Being with a woman if she was of lower social rank would have made you, as a man, less than a man while having a male lover of equal worth brought you honour. While they most likely were lovers then they would not call themselves gay; it was simply natural to have sex with people of both gender.
Both men married, Alexander married several women but their love stayed.
If asked they would have said their were friends; a word that meant so much more then when we say 'we're friends' today.
Friends meant they trusted each other and would always support each other.
But being lovers as well would not be how they defined their relationship; soulmates maybe.
And if confronted by the homophobic world today and all those questions about his sex life Alexander would have been confused.
Alexander was a King, a conquor and a friend first. Whom he bedded need not be who he loved but for Hephaestion this was true.
But Alexander would have focused on the love between them, the friendship; not the sex.

On Hephaistion and his relationship the offical Alexander webpage says this:
Hephaistion was a Macedonian nobleman, closest friend and alledged lover of Alexander the Great. Born in Pella, the capital of Macedonian, Hephaistion was educated at the court of King Philip and became a childhood friend of Alexander. It was commonplace in this era for men to have male lovers although Alexander's mother Olympias was very jealous of his relationship with Hephaistion. The envy of all the court officials made Hephaistion an isolated man, dependent on and totally loyal to Alexander. Hephaistion accompanied Alexander the Great on many of his victorious battles, however, it is probable that Hephaistion was a better strategist and diplomat than commander. Hephaistion was Alexander's best man when he married Roxane, his first wife. In 324 B.C. Hephaistion fell ill and died. Alexander was shocked and grieved bitterly for Hephaistion, the person who had been closest to his heart.
- from Alexander The Great.


Read a history professor's view on this:

Hephaistion - Alexander's lover?

Disclaimer: "Alexander", Alexander, Hephaestion, and all things Alexander belong to Oliver Stone and Warner Brothers and I intend no infringement and I make no money of it.