This dissertation presents a study of wave-particle interactions in space and in the laboratory. To be concrete, the excitation of whistler-mode chorus waves in space and in the laboratory is studied in the first part. The relaxation of whistler anisotropy instability relevant to whistler-mode chorus waves in space is examined. Using a linear growth rate analysis and kinetic particle-in-cell simulations, the electron distributions are demonstrated to be well-constrained by the whistler anisotropy instability to a marginal-stability state, consistent with measurements by Van Allen Probes. The electron parallel beta $\beta_{\parallel e}$ separates the excited whistler waves into two groups: (i) quasi-parallel whistler waves for $\beta_{\parallel e} \gtrsim 0.02$ and (ii) oblique whistler waves close to the resonance cone for $\beta_{\parallel e} \lesssim 0.02$. The saturated magnetic field energy of whistler waves roughly scales with the square of the electron beta $\beta_{\parallel e}^2$, as shown in both satellite observations and particle-in-cell simulations. Motivated by the puzzles of chorus waves in space and by their recognized importance, the excitation of whistler-mode chorus waves is studied in the Large Plasma Device by the injection of a helical electron beam into a cold plasma. Incoherent broadband whistler waves similar to magnetospheric hiss are observed in the laboratory plasma. Their mode structures are identified by the phase-correlation technique. It is demonstrated that the waves are excited through a combination of Landau resonance, cyclotron resonance and anomalous cyclotron resonance. To account for the finite size effect of the electron beam, linear unstable eigenmodes of whistler waves are calculated by matching the eigenmode solution at the boundary. It is shown that the perpendicular wave number inside the beam is quantized due to the constraint imposed by the boundary condition. Darwin particle-in-cell simulations are carried out to study the simultaneous excitation of Langmuir and whistler waves in a beam-plasma system. The electron beam is first slowed down and relaxed by the rapidly growing Langmuir wave parallel to the background magnetic field. The tail of the core electrons are trapped by the large amplitude Langmuir wave and are accelerated to the beam energy level in the parallel direction. The excitation of whistler waves through Landau resonance is limited by the saturation of Langmuir waves, due to a faster depletion rate of the beam free energy from $\partial f_b /\partial v_{\parallel} > 0$ by the latter compare to the former. The second part of the thesis considers the interaction between electromagnetic ion cyclotron (EMIC) waves and relativistic electrons. Nonlinear interactions between them are investigated in a two-wave oscillator model. Three interaction regimes are identified depending on the separation of the two wave numbers. Both the decoupled and degenerate regimes are characterized by phase bunching, in which the resonant electrons are scattered preferentially to one direction rather than diffusively. In the coupled regime, resonant electrons experience alternate trapping and de-trapping near the separatrix, from which stochastic motion of electrons arises. For a continuous spectrum of EMIC waves, test particle simulations are compared against quasi-linear diffusion theory (QLT) description of the wave-particle interactions. QLT gives similar results as test particle simulations for the small amplitude and broadband waves, whereas it fails for large amplitude and narrowband waves. By varying the wave spectral width and wave intensity systematically, a regime map is constructed to indicate the applicability of QLT in the wave parameter space.