Analogue gravity is a research program that investigates analogues of general relativistic gravitational fields in other physical systems, particularly condensed matter systems, to gain insights into their corresponding problems. This review discusses the history, aims, results, and future prospects of various analogue models. It starts with a simple example of an analogue model, then explores the rich history and complex tapestry of models discussed in the literature. The last decade has seen significant development of analogue gravity ideas, leading to numerous publications, a workshop, two books, and this review article. Future prospects for the programme are promising, both experimentally and theoretically. Analogue models of gravity have a long history, dating back to the early years of general relativity. One of the most well-known analogies is the use of sound waves in a moving fluid as an analogue for light waves in curved spacetime. Supersonic fluid flow can generate a "dumb hole," the acoustic analogue of a black hole, and the analogy can be extended to demonstrate phononic Hawking radiation from the acoustic horizon. This provides a concrete laboratory model for curved-space quantum field theory. Analogue models are useful for both experimental and theoretical reasons. They provide insights into perplexing theoretical questions and allow for bidirectional information flow between general relativity and analogue models. The list of analogue models is extensive, and this review seeks to do justice to both the key models and their features. The simplest example of an analogue spacetime is acoustics in a moving fluid. The basic physics is simple, and the conceptual framework is straightforward. The velocity of a sound ray propagating in a fluid is given by the equation $ \frac{d\mathbf{x}}{dt} = c\mathbf{n} + \mathbf{v} $, where $ c $ is the speed of sound and $ \mathbf{v} $ is the fluid velocity. This leads to a sound cone in spacetime defined by the condition $ n^2 = 1 $. In physical acoustics, the derivation of the analogy holds in a more restricted regime, but it can uniquely determine a specific effective metric and accommodate a wave equation for sound waves. The acoustic metric is derived from the fluid dynamics equations and is related to the distribution of matter in a simple algebraic fashion. The acoustic metric has a signature of $ (-, +, +, +) $, and it inherits key properties from the underlying flat physical metric. The acoustic geometry can inherit the topology of the physical metric and has important properties such as "stable causality." The acoustic metric can be used to define horizons, ergo-regions, and surface gravity, which are important features of general relativity. The surface gravity is defined by the norm of the four-acceleration of fiducial observers and is related to the acceleration of the fluid as it crosses the horizon. The Hawking temperature is related to the surface gravity and the speed of sound at the horizonAnalogue gravity is a research program that investigates analogues of general relativistic gravitational fields in other physical systems, particularly condensed matter systems, to gain insights into their corresponding problems. This review discusses the history, aims, results, and future prospects of various analogue models. It starts with a simple example of an analogue model, then explores the rich history and complex tapestry of models discussed in the literature. The last decade has seen significant development of analogue gravity ideas, leading to numerous publications, a workshop, two books, and this review article. Future prospects for the programme are promising, both experimentally and theoretically. Analogue models of gravity have a long history, dating back to the early years of general relativity. One of the most well-known analogies is the use of sound waves in a moving fluid as an analogue for light waves in curved spacetime. Supersonic fluid flow can generate a "dumb hole," the acoustic analogue of a black hole, and the analogy can be extended to demonstrate phononic Hawking radiation from the acoustic horizon. This provides a concrete laboratory model for curved-space quantum field theory. Analogue models are useful for both experimental and theoretical reasons. They provide insights into perplexing theoretical questions and allow for bidirectional information flow between general relativity and analogue models. The list of analogue models is extensive, and this review seeks to do justice to both the key models and their features. The simplest example of an analogue spacetime is acoustics in a moving fluid. The basic physics is simple, and the conceptual framework is straightforward. The velocity of a sound ray propagating in a fluid is given by the equation $ \frac{d\mathbf{x}}{dt} = c\mathbf{n} + \mathbf{v} $, where $ c $ is the speed of sound and $ \mathbf{v} $ is the fluid velocity. This leads to a sound cone in spacetime defined by the condition $ n^2 = 1 $. In physical acoustics, the derivation of the analogy holds in a more restricted regime, but it can uniquely determine a specific effective metric and accommodate a wave equation for sound waves. The acoustic metric is derived from the fluid dynamics equations and is related to the distribution of matter in a simple algebraic fashion. The acoustic metric has a signature of $ (-, +, +, +) $, and it inherits key properties from the underlying flat physical metric. The acoustic geometry can inherit the topology of the physical metric and has important properties such as "stable causality." The acoustic metric can be used to define horizons, ergo-regions, and surface gravity, which are important features of general relativity. The surface gravity is defined by the norm of the four-acceleration of fiducial observers and is related to the acceleration of the fluid as it crosses the horizon. The Hawking temperature is related to the surface gravity and the speed of sound at the horizon