Raven and Beast Boy have a very complicated relationship, despite that the two are polar opposites in terms of personality. Raven is collected, down to earth and cold, while Beast Boy is cheerful, laid-back and energetic. Plus Raven likes to read, while Beast Boy really doesn't. He is a video game kind of guy.
They often fight and get on each other's nerves: Raven's cold demeanor and "creepiness" annoy Beast Boy and she is often irritated by his bad jokes and immaturity. Although, in the beginning, they have a rough relationship, they become closer and continue to develop their friendship throughout the series.
Beast Boy often gets irritated by Raven's sarcastic remarks to him, but throughout the series, never gives up on trying to make her smile or laugh. He even openly admits his quest to never stop making jokes until Raven smiles in Aftershock - Part 1.