We review here some of our very recent contributions to nonlinear dynamics in three different system configurations. They all share common features: mode competition, cavity and time-delay instability. First, we report on peculiar polarization switching and mode hopping properties of quantum dot vertical-cavity surface-emitting lasers (VCSELs). Polarization competition and corresponding bistable hopping dynamics is found in a large range of injection currents and with statistical properties of the dwell time being significantly different from those reported in quantum well VCSELs. Secondly, we analyze several schemes that aim at multiplexing chaos between pairs of synchronized lasers, hence of recovering individually transmitted data carried by a single chaotic signal. These schemes making use of active passive decomposition or multiple time-delays allow for an efficient use of the large chaotic bandwidth in chaos based communications. Finally, we summarize our contributions to the control of modulation instability leading to optical pattern formation. Our system is made of a photorefractive nonlinear crystal in a single feedback experiment. The use of an optically-induced photonic lattice makes it possible to control the spatial modes and leads to either forcing of the pattern, seeding of new spatial modes, or photonic band-gap manipulation. In a misaligned feedback experiment, drifting patterns and transition from convective to absolute instabilities are observed. Interestingly, rotating optical patterns are reported in the case of counter-propagating vortex beams.