I will discuss recent large data results concerning nonlinear systems of wave equations of the so-called energy critical class, obtained using the concentration compactness method. This involves results on critical wave maps as well as critical MKG equations. In particular, we discuss a recent novel result on critical radial wave maps with target $S^m$, obtained jointly with E. Chiodaroli and J. Luhrmann. Speaker(s): Joachim Krieger (EPFL Lausanne, Switzerland)