A self-oscillator generates and maintains a periodic motion at the expense of an energy source with no corresponding periodicity. Small perturbations about equilibrium are negatively damped, leading to instability of the linear equations of motion. Non-linearity accounts for the steady-state oscillation and for the ability of coupled self-oscillators to exhibit spontaneous synchronization ("entrainment") and chaos. The theory of self-oscillators has achieved its greatest sophistication in control theory and in the theory of ordinary differential equations. I shall explain why an understanding better suited to the needs of engineers and physicists is based on considerations of energy, efficiency, and irreversibility. After reviewing how forced and parametric resonances are described by energy flow into a driven oscillator, I shall explain how a simple example of self-oscillation (the swaying of the London Millennium Footbridge in 2000) results from positive feedback between the oscillation and an external energy source (the motion of pedestrians on the bridge). I shall explain how the nonlinearity of self-oscillators connects to entrainment and to the thermodynamic irreversibility of motors, before commenting on how this approach throws new light on concrete problems, like the maintenance of the Chandler wobble in geophysics. This presentation will be based on the review article A. Jenkins, Phys. Rep. 525, 167 (2013), and a book currently in preparation.