We will present a survey on our experimental and theoretical studies of polarization dynamics in vertical-cavity surface-emitting lasers (VCSELs) when subject to orthogonal optical injection, i.e. the injected field has a linear polarization (LP) orthogonal to that of the free-running VCSEL. The output characteristics of an oxide-confined AlGaAs-GaAs quantum well VCSEL are experimentally mapped as a function of the strength of the optical injection and the detuning between the injection frequency and the free-running frequency of the solitary laser. Experimentally, we achieve a very large range of frequency detunings: from -82 to 89 GHz. Two border lines at negative and positive detunings form "a tongue" of polarization switch (PS) region; its area expanding to both positive and negative detunings with increasing the injection strength. The two border lines are with a well pronounced region of bistability, the hysteresis width is almost constant for positive detuning and increasing for negative ones. Only in the later case the route to PS occurs through injection locking (both the polarization and the frequency of the VCSEL locks to the ones of the master laser). The route to injection locking can be accompanied by a rich nonlinear dynamics, including limit cycle, wave mixing, subharmonic resonance and possibly period doubling route to chaos. The PS "tongue" is further strongly influenced at large positive detuning, which we identify as being due to an injection locking of the first-order transverse mode of the VCSEL. We carry out theoretical studies of the case of orthogonal injection in VCSELs, which qualitatively match the experimental findings. Furthermore, we predict the existence of new injection locked solution for which the two LP modes both lock to the master laser frequency resulting in an elliptically polarized injection locked (EPIL) steady-state. Modern continuation techniques allow us to unveil an unfolding mechanism of the EPIL solution as the detuning varies and also to link the existence of the EPIL solution to a resonance condition between the master laser frequency and the frequency of the suppressed VCSEL LP mode. This EPIL solution may coexist with the LP injection locked solution, resulting in a new type of bistability in VCSELs