Coupled mode theory considers the interaction between eigensolutions of a system (modes). It is a theoretical framework that underlies many physical phenomena, such as coupled optical cavities and waveguides, cavity optomechanics or the coupling between atoms and cavities. We derive the coupled-mode equations for a system of harmonic oscillators and transform them into Bloch equations, which allows us to represent the solutions on the Bloch sphere. We discuss mode coupling (hybridization) and coherent control protocols, such as Ramsey interferometry and dispersive coupling. We consider time-dependent interactions and analyze adiabatic and diabatic transitions (Landau-Zener tunneling). The control of damping brings us to topics such as time-reversal symmetry breaking, exceptional points and non-Hermitian dynamics. We discuss the limits of ultrastrong coupling and nonlinear interactions and analyze the phenomenon of induced transparency. Finally, we analyze the dynamics of optomechanical systems and discuss the transition to multimode systems and quantum mechanics.