The spatio-temporal dynamics of high-power semiconductor lasers are studied theoretically on the basis of space-dependent microscopic semiconductor-Maxwell-Bloch model equations. In the free-running broad-area and multi-stripe semiconductor lasers, complex spatio-temporal patterns are observed as a result of self-focusing, filamentation and transverse modulational instabilities in space-time images of the near-field output intensity. It is the irregular, possibly chaotic, dynamics of the filaments which are responsible for the generally much inferior beam quality and spectral characteristics of the high-power broad-area lasers when compared to common semiconductor lasers with moderate output power. The inherent coupling of optical diffraction with carrier transport processes leads to the formation of the spatio-temporal patterns. The simultaneous relevance of spectral and spatial hole-burning phenomena is manifested in the space- and time-dependence of the optical near-field showing, at the same time, spatio-temporal and spectral-temporal variations in the sub-ps range.