The arrogant, handsome intern who we first got to know as the man's man, both repulsive and irresistible to Izzie. The two had an on-again, off-again relationship that ended as Alex got caught sleeping with a nurse - in an attempt to regain confidence after "performance anxiety" problems with Izzie.
A former wrestler at the University of Iowa, he often tries to act more tough and aloof than he actually is. He and George O'Malley often clash due to their different personalities and also because Alex indirectly gave him syphilis (in Season One, George dated and slept with Olivia, the same nurse that Alex shagged).
After he and a visiting surgeon (Mark Sloan, the former best friend of Derek and lover of Addison) discussed his career prospects, Alex expressed interest in becoming a plastic surgeon. He gets that chance in Season Three, when Mark becomes a member of the staff - and makes Alex his personal lackey.
That means Alex Karev gets to know more about coffee than surgery. But he takes refuge on the "vagina squad" with Addison Montgomery, another attending who starts to fall for him before he turns her away. Later, he almost falls for a patient with a case of amnesia, but can't bring himself to commit to her either.
Will this patient - Rebecca Pope (also known as Ava, or Jane Doe) be the one to bring Alex Karev out of his shell at long last?