In season eight, Beckett is promoted to Captain and made Commanding Officer of the 12th Precinct.
Even though Beckett does date (and subsequently break up with) several different men during her partnership with Castle, she eventually develops feelings for him, though she is reluctant to acknowledge them openly to anyone.
Her reluctance to acknowledge her feelings for Castle, as well as her rejection of her previous boyfriends, stems from her determination to not get hurt, especially in the aftermath of her mother's death.
Alexis is very close to her father, as they do many activities together, including fencing, book research projects such as learning lock-picking and safe-cracking—and laser tag.
She has also developed a certain bond with Beckett, asking Beckett's advice when contemplating going on an exchange trip to France, and making arrangements with the detective to spend three days working at the police station as part of a project for her civics class.
When the series begins, Castle has decided to kill off his most famous character, Derrick Storm, because the character has become boring to him.