The adoptive sister of Eren and mutual childhood friend of Armin, Mikasa hides her emotions but cares deeply for Eren--never hesitating to cry with tears of joy or despair depending on what happens to him. She shares an unbreakable bond with Eren following events in their past, and his mother requesting that she protect him made her even more overly protective of him than she was beforehand.
Subtle (and not-so-subtle) hints throughout the manga suggest she loves Eren as a woman, rather than as a sister. However, in the first four volumes he hasn't shown any such feelings in return, and it seems her feelings are destined to be unrequited.
When Mikasa's parents were murdered, and she was tied-up on the floor, Eren saved her life - when visiting by chance with his father - by killing two of the three men who killed her parents, in spite of him only being a child at the time. And then, when the third man was strangling a helpless Eren after catching him off-guard, she picked up a knife off the floor and stabbed the man in the back; killing him.
Afterward, Eren gave Mikasa his scarf - which, even many years in the future, she still wears - and made sure she understood that he, and his parents, were now her family. Because of his heroics and this gesture, she feels her life is Eren's now, because - in her mind - she already died once.
Eren's best friend, he is physically and emotionally weak. His strategic abilities have saved Eren and Mikasa several times. He himself does not notice the things he does for Eren and Mikasa, and believes himself to be completely incompetent and hates himself for having to rely of Eren and Mikasa.
Shingeki's protagonist. His adoptive sister, Mikasa, notes on numerous occasions that he acts on impulse without thinking things through, and she often pulls/carries/throws him when he starts fighting with others to protect him from himself. Along with Mikasa, he tends to spend his free time with their mutual friend, Armin.
When Erin was a child, he saved Mikasa from being killed when visiting her home with his father. Three men - killers of her parents - were in her house, and he killed two of them--one by slitting his throat and the other by charging at with a quickly assembled spear. Mikasa herself killed the third man when he attempted to strangle Erin. After this, he gave Mikasa his scarf and took her into his family.
Later, when the giants invaded his home, he could only watch on as his mother - trapped under the rubble of their house - was eaten by a giant. This event made him swear that he'd kill every giant and not live a life cowering in fear.
Sometime after this - before the timeskip that jumped a few years ahead, to when he became a soldier - his father injected him with something. It's unknown what at this time but it turns out, because of the injection, Erin can regenerate lost limbs and transform into a somewhat out of control giant.
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