In this talk I focus on superlattices and double barrier resonant tunneling structures, which are prominent examples of semiconductor nanostructures. I demonstrate that nonlinear charge transport in these systems exhibits a variety of spatio-temporal instabilities and pattern formation processes . Models will be developed and analyzed with respect to spatio-temporal patterns of the current density and electric field distribution. In particular, I will emphasize some features which are ubiquitous in complex nonlinear dynamic systems of different nature: the role of global couplings, spatio-temporal chaos, the control and selection of multistable patterns, synchronization and autosynchronization by time-delayed feedback (chaos control).
 E. Schöll: Nonlinear spatio-temporal dynamics and chaos in semiconductors, Cambridge University Press (2001).