  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 $\ell_2$
implies presence of expander-like structures? (b) To what extent $\ell_2$ is
the most difficult space to embed into?
