  In recent years, observations of the Sunyaev-Zeldovich (SZ) effect have had
significant cosmological implications and have begun to serve as a powerful and
independent probe of the warm and hot gas that pervades the Universe. As a few
pioneering studies have already shown, SZ observations both complement X-ray
observations -- the traditional tool for studying the intra-cluster medium --
and bring unique capabilities for probing astrophysical processes at high
redshifts and out to the low-density regions in the outskirts of galaxy
clusters. Advances in SZ observations have largely been driven by developments
in centimetre-, millimetre-, and submillimetre-wave instrumentation on
ground-based facilities, with notable exceptions including results from the
Planck satellite. Here we review the utility of the thermal, kinematic,
relativistic, non-thermal, and polarised SZ effects for studies of galaxy
clusters and other large scale structures, incorporating the many advances over
the past two decades that have impacted SZ theory, simulations, and
observations. We also discuss observational results, techniques, and
challenges, and aim to give an overview and perspective on emerging
opportunities, with the goal of highlighting some of the exciting new
directions in this field.
