The term bioconvection describes hydrodynamic instabilities and pattern formation resulting from concentration gradients of biased swimming micro-organisms in suspension. To systematically scale-up from individuals to a population-level description of a suspension it is necessary to understand in detail mechanisms for individual behaviour. Here, I shall describe current modelling approaches and discuss some of the outstanding issues and challenges. To help address some of these I shall present a selection of results on dispersion, phototaxis, resonant alignment in oscillatory flows and non-modal stability.