Blast–obstacle interaction is a complex, multi-faceted problem. Whilst engineering-level tools exist for predicting blast parameters (e.g. peak pressure, impulse and loading duration) in geometrically simple settings, a blast wave is fundamentally altered upon interaction with an object in its path, and hence, the loading parameters are themselves affected. This article presents a comprehensive review of key research in this area. The review is formed of five main parts, each describing: the direct loading of a blast wave on the surface of a finite-sized structure; the modified pressure of the blast wave in the wake region of three main obstacle types – blast walls, obstacles, wall/obstacle hybrids; and finally, a brief description of some methods for predicting loading parameters in such blast–obstacle interaction settings. Key findings relate to the mechanisms governing blast attenuation, for example, diffraction, reflection (diverting away from the target structure), expansion/volume increase, vortex creation/growth, as well as obstacle properties influencing these, such as porosity (blockage ratio), obstacle shape, number of obstacles/rows, arrangement and surface roughness.