**1. Introduction**

The topology optimisation method originates from the field of solid mechanics, where it emerged from sizing and shape optimisation by the end of the 1980s. The seminal paper on topology optimisation is often quoted as being the homogenisation method by Bendsøe and Kikuchi [1]. Topology optimisation is posed as a material distribution technique that answers the question "where should material be placed?" or alternatively "where should the holes be?". As a structural optimisation method, it distinguishes itself from the more classical disciplines of sizing and shape optimisation, by the fact that there does not need to be an initial structure defined a priori. Having stated that, we define topology optimisation slightly wider in this context, as we include optimisation approaches in which the topology is allowed to or can change during the optimisation process. The review papers by Sigmund and Maute [2] and Deaton and Grandhi [3] give a general overview of topology optimisation methods and applications. Today, topology optimisation for solid mechanics is a mature technology that is widely available in all major finite element analysis (FEA) packages and even in many computer aided design (CAD) packages. The technology is utilised at the component design level in the automotive and aerospace industries.

The ideas of the original methodology are extendable to all physics, where the governing equations can be described by a set of partial differential equations (PDEs). It has therefore in the post-2000 decades seen widespread application to a range of different physics, such as acoustics, photonics, electromagnetism, heat conduction, fluid flow, etc. [3].

When applied to fluid problems, the question should be rephrased from "where should the holes be?" to "where should the fluid flow?". The optimisation problem basically becomes a question of where to enforce relevant boundary conditions for the flow problem. This review paper is a survey of published papers containing topology optimisation of fluid flow problems and related fluid-based problems. It is the first to cover the entire history, from its very beginning to the current state of the art. There are two previous review papers dealing with two different subsets under the umbrella of fluid-based problems, namely microfluidics [4] and thermofluidics [5].
