The main purposes of this paper are (1) To survey the area of coarse embeddability of metric spaces into Banach spaces, and, in particular, coarse embeddability of different Banach spaces into each other; (2) To present new results on the problems: (a) Whether coarse non-embeddability into l2 implies presence of expander-like structures? (b) To what extent l2 is the most difficult space to embe...