We report on experimental and theoretical results showing how mode competition in quantum dot semiconductor lasers can result in new nonlinear dynamics. A first example is a competition between non-orthogonal elliptically polarized modes that manifests itself in a polarization switching at a given injection current and in a polarization mode hopping dynamics at different time-scales. A second example is a pulsating dynamics in a quantum dot laser with optical injection, which originates from the simultaneous lasing in the ground and excited modes.