Castle and Beckett finally get together in the Season 4 finale of "Castle." After four seasons of buildup and romantic tension, they act on their feelings and spend the night together, marking the official start of their relationship.
They had a long "will they or won't they" dynamic before this moment, with Castle pursuing Beckett and both experiencing jealousy and mixed feelings throughout the first three seasons. Their relationship dynamics evolve with ups and downs until this key turning point in Season 4.