Chirps (i.e., transient AM-FM waveforms) are ubiquitous in nature and man-made systems, and they may serve as a paradigm for many nonstationary deterministic signals. The time-frequency plane is a natural representation space for chirps, and we will here review a number of questions related to chirps, as addressed from a time-frequency perspective. Global and local approaches will be described for matching and/or adapting representations to chirps. As a corollary, joint time-frequency descriptions of chirps will be shown to allow for effective definitions of instantaneous frequencies via localized trajectories on the plane. A number of applications will be mentioned, ranging from bioacoustics to turbulence and gravitational waves.