  We survey results about exact cylindrically symmetric models of gravitational
collapse in General Relativity. We focus on models which result from the
matching of two spacetimes having collapsing interiors which develop trapped
surfaces and vaccum exteriors containing gravitational waves. We collect some
theorems from the literature which help to decide a priori about eventual
spacetime matchings. We revise, in more detail, some toy models which include
some of the main mathematical and physical issues that arise in this context,
and compute the gravitational energy flux through the matching boundary of a
particular collapsing region. Along the way, we point out several interesting
open problems.
