Kaz is essentially the head of the Dregs, a Ketterdam street gang, and the Crow Club, a local gambling den. He is a skilled criminal who can evade capture and take on perilous assignments. He is perceived as something other than human and heartless, rumours he is glad to spread. As we've learned more about Kaz, I've grown to appreciate him even more.
To most people, Inej is just The Wraith. Raised as an acrobat, she is now a spy for Dregs and Kaz. Inej's work requires her to learn everyone's secrets, so she does. She hopes to reunite with her loved ones one day, but the pain of the past prevents her from doing so with any certainty.
A Dreg marksman like Jesper is rare. Because of his inability to avoid betting, especially on games, he will always owe money to the Dregs. He's a natural shot and can't stand being without his firearms. I'd want Jesper on my side if a gunfight broke out.
Nina belongs to the Dregs as a Heartrender. Her skills make her a very important Grisha asset. She has the ability to heal slightly and manipulate emotions in addition to stopping a heart. She is free to return to Ravka whenever she likes, but something is keeping her in Ketterdam.
The fugitive Wylan is someone Kaz has decided may be beneficial. Even if the rest of the crew doesn't know what to make of him, his connections in Ketterdam make him useful.
Convicted of the crime of existence, Matthias is a Fjerdan sent to track down and kill Grisha. He acts in his own self-interest, whether it is out of vengeance or any other motive. Truthfulness characterises what he says.