Summary: Bioconvection patterns are usually observed in the laboratory in shallow suspensions of randomly, but on average upwardly, swimming micro-organisms which are a little denser than water, but have also been found in situ in micropatches of zooplankton [\textit{U. Kils}, Bull. Mar. Sci. 53, 160--169 (1993)]. The mechanism of upswimming differs between bottom-heavy algae and oxytactic bacteria. Rational continuum models have been formulated and analysed in each of these cases for low cell volume fraction. These will be described, as will new theoretical and experimental developments, including nonlinear analysis of the patterns, dispersion in shear flows, measurements of algal cell swimming behaviour, and new attempts to set up a model for more concentrated suspensions. The paper will review all work in this area since 1992, the year of the publication of the article ``Hydrodynamic phenomena in suspensions of swimming micro-organisms'' by \textit{T. J. Pedley} and \textit{J. O. Kessler} [Annu. Rev. Fluid Mech. 24, 313--358 (1992)].