Resonant interactions between waves and particles play major roles in high-temperature, or collisionless plasmas. They often lead to the self-trapping of charged particles by their own electrostatic potential, which is a kinetic, nonlinear effect. This self-trapping leads to a formation of structures resembling vortices, in the phase-space of the particle distribution function (real space + velocity space). Understanding the dynamics of these structures in phase-space can help clarify the mechanisms of phenomenon that may seem counter-intuitive from the point-of-view of an observer in real-space. When many phase-space structures of various scales coexist and interact, they form what we may call as phase-space turbulence, which must be described by a statistical approach. In my talk, I introduce concepts of phase-space turbulence [1], and its relationship with quasilinear and resonance-broadening theories. In this talk, I review these phenomena based on three types of waves: waves driven by supra-thermal particles in fusion plasmas [2], ion-acoustic waves in homogeneous plasmas [3], and drift-waves driven by trapped particles in tokamaks [4]. I describe the impact of phase-space structures on stability and the nonlinear evolution of waves, as well as turbulence properties, particle transport, anomalous resistivity, and turbulent heating. I propose experimental applications of phase-space structures as diagnostic and mean of control. References: [1] P.H. Diamond, Y. Kosuga, M. Lesur, in book Rotation and Momentum Transport in Magnetized Plasmas, Aix-en-Provence (2015). [2] M. Lesur, Y. Idomura, Nucl. Fusion 52 (2012) 094004. [3] M. Lesur, et al., Plasma Phys. Control. Fusion 56 (2014) 075005. [4] J. Médina, et al., Phys. Plasmas 25 (2018) 122304.