This review is devoted to studies of quantum optics effects for quantum emitters (QEs) in the near field of nanoparticles (NPs). In the simple model of a two-level QE located near a plasmon NP, we analyze the mechanisms for modifying the radiative and nonradiative decay rates and discuss the distribution of the near-field intensity and polarization around the NP. This distribution has a complex structure, being significantly dependent on the polarization of the external radiation field and on the parameters of NP plasmon resonances. The quantum optics effects in the system (NP+QE+external laser field) are analyzed, including the near-field modification of the resonance fluorescence spectrum of a QE, the bunching/antibunching effects and photon quantum statistics effects in the spectrum, the formation of squeezed light states, and quantum entangled states in such systems.