We report on the dynamics of the polarization modes and high order transverse modes that occur when VCSELs are subject to optical injection. Several dynamical scenarios shall be discussed and compared to those typically encountered in conventional laser problems using edge-emitting lasers. In particular the two polarization mode competition that typically underlies VCSEL light emission induces new injection-locking steady states and modifies the bifurcation that delimits the injection locking boundaries. Depending on the injection strength and master-slave frequency detuning, polarization switching and transverse mode switching can be observed and accompanied by dynamical instabilities (period doubling, chaos etc.). Theoretical analysis based on continuation of VCSEL models will be compared with experimental observations. Finally we shall report on the influence of polarization mode competition on the synchronization of unidirectionally coupled VCSELs and its use for chaos secure communication systems.