  We review selected recent results concerning the global structure of
solutions of the vacuum Einstein equations. The topics covered include
quasi-local mass, strong cosmic censorship, non-linear stability, new
constructions of solutions of the constraint equations, improved understanding
of asymptotic properties of the solutions, existence of solutions with low
regularity, and construction of initial data with trapped surfaces or apparent
horizons.
  This is an expanded version of a plenary lecture, sponsored by Classical and
Quantum Gravity, held at the GR17 conference in Dublin in July 2004.
