A small fraction of cosmic microwave background (CMB) photons scatter off electrons in the ionised gas in collapsed structures. This process, known as the Sunyaev-Zel'dovich effect, is usually broken down into a thermal (tSZ) and a kinematic (kSZ) contribution. While the former is sensitive to the random velocities of the electrons in the hot gas, the latter is sourced by the bulk motion of the entire object. In this thesis I measure the signature of both of these effects by cross-correlating CMB data with different tracers of the large-scale structure. I further study how these effects can be used as probes of cosmology and astrophysics. I first report a statistically significant detection of the kSZ effect. This is achieved by combining a cluster catalogue derived from the first year data of the Dark Energy Survey with CMB temperature maps from the South Pole Telescope. I perform the measurement with a differential statistic that isolates the pairwise kSZ signal, providing the first detection of the large-scale motion of clusters using redshifts derived from photometric data. By fitting the pairwise kSZ signal to a theoretical template, I measure the average central optical depth of the cluster sample. I compare the extracted signal to simulations and find good agreement with respect to the signal-to-noise, the constraint on the optical depth, and the corresponding gas fraction. I next study the potential of the kSZ effect as a probe of cosmology, again focussing on the pairwise method. The main challenge is disentangling the cosmologically interesting mean pairwise velocity from the cluster optical depth and the associated uncertainties on the baryonic physics in clusters. Using the Magneticum cosmological hydrodynamical simulations I calibrate a scaling relation between the amplitude of the tSZ signal and the optical depth. I show that this relation can be used to recover an accurate estimate of the mean pairwise velocity from the kSZ signal, and that this effect can therefore be used as a probe of cosmology. I finally derive constraints on feedback from active galactic nuclei by setting limits on their tSZ signal. By combining all-sky microwave, sub-mm, and far-infrared data from the Planck and AKARI satellites, I break the degeneracy between the tSZ signature and extragalactic dust emission. I test the measurement pipeline with a catalogue of galaxy clusters, finding the expected high-significance tSZ detection together with correlated dust emission. I then measure the tSZ signal of spectroscopically confirmed quasi-stellar objects (QSOs), but obtain only a low-significance hint of a tSZ signature. This analysis leads to a lower mean thermal energy than reported in some previous studies which were contaminated by dust emission. A comparison of these results to hydrodynamical simulations can be used as a probe of QSO host masses.