Nonlinear dynamics of Vertical-Cavity Surface-Emitting Lasers (VCSELs) induced by optical injection, optical feedback, current modulation and mutual coupling is reviewed. Due to the surface emission and cylindrical symmetry VCSELs lack strong polarization anisotropy and may undergo polarization switching. Furthermore, VCSELs may emit light in multiple transverse modes. These VCSEL properties provide new features to the rich nonlinear dynamics induced by an external perturbation. We demonstrate for the case of orthogonal optical injection that new Hopf bifurcation on a two-polarization-mode solution delimits the injection locking region and that polarization switching and injection locking of first-order transverse mode lead to a new resonance tongue for large positive detunings. Similarly, the underlying polarization mode competition leads to chaotic-like behavior in case of gain switching and the presence of two transverse modes additionally reduces the possibility of regular dynamics. The bistable property of VCSEL makes it possible to investigate very fundamental problems of bistable systems with time-delay, such as the coherence resonance phenomenon. We also demonstrate that the synchronization quality between unidirectionally coupled VCSELs can be significantly enhanced when the feedback-induced chaos in the master laser involves both orthogonal LP fundamental transverse modes. 1. Introduction The change of the semiconductor laser cavity geometry from facet to surface-emitting gave birth to the vertical-cavity surface-emitting lasers (VCSELs) [1] with significant advantages, such as single longitudinal mode emission, low cost, circular output beam, and easy fabrication in two-dimensional arrays. As a result, VCSELs are nowadays substituting the traditional semiconductor edge emitting lasers (EELs) in many applications, such as fiber to the home links, computer networks, optical interconnects, and optical sensing. Until recently, most of the commercially available VCSELs were emitting in the near infrared, around 850？nm or 970？nm, based on GaAs active region and GaAs/AlGaAs DBR mirrors but now they become available also at telecommunication wavelengths 1.3 or 1.55？μm and at visible or even UV wavelengths. Emission in multiple transverse modes is usually found in VCSELs [2] as a result of spatial hole burning effect [3, 4]. Furthermore, due to the surface emission and cylindrical symmetry VCSELs grown on (001) substrate lack strong polarization anisotropy and may undergo polarization switching (PS) [2, 5]. Different physical mechanisms can lead to
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