The cellular detail of blood is an essential factor in its flow, especially in vessels or devices with size comparable to that of its suspended cells. This article motivates and reviews numerical simulation techniques that provide a realistic description of cell-scale blood flow by explicitly representing its coupled fluid and solid mechanics. Red blood cells are the principal focus because of their importance and because of their remarkable deformability, which presents particular simulation challenges. Such simulations must couple discretizations of the large-deformation elasticity of the cells with the viscous flow mechanics of the suspension. The Reynolds numbers are low, so the effectively linear fluid mechanics is amenable to a wide range of simulation methods, although the constitutive models and geometric factors of the coupled system introduce challenging nonlinearity. Particular emphasis is given to the relative merits of several fundamentally different simulation methods. The detailed description provided by such simulations is invaluable for advancing our scientific understanding of blood flow, and their ultimate impact will be in the design of biomedical tools and interventions.