Cylindrical vector beams (CVBs), characterized by their spatially varying polarization and axial symmetry, have emerged as powerful tools for engineering light-matter interactions at the nanoscale. Unlike conventional linearly polarized beams, tightly focused CVBs can generate strong longitudinal electric or magnetic field components, enabling the selective excitation of specific multipolar modes and various resulting modes in optical nanostructures. This unique field configuration facilitates the excitation of various optical phenomena such as anapole states, dark modes, Fano resonances, optical magnetism, enhanced nonlinear optical responses, etc., which are challenging to achieve with traditional illumination. In this review, we summarize recent advancements in nanophotonic phenomena/effects driven by CVB excitation, illustrated through seminal studies in plasmonic, dielectric, or hybrid nanostructures, offering promising opportunities for applications in imaging, sensing, optical trapping, quantum information processing, etc. We discuss how enhanced electromagnetic field confinement, increased coupling efficiency, and precise control over resonant scattering can lead to novel nanophotonic phenomena/effects under CVB illumination. The insights presented here aim to guide future developments in structured light-matter interaction and inspire the design of advanced nanophotonic systems.