Convection in an imposed vertical magnetic field can lead to localised states in domains of large horizontal extent. This phenomenon can be seen as an instability of convection rolls that arises naturally from the fact that the magnetic flux through the layer is conserved. Nonlinear states in two dimensions can be found involving only a single convection cell (known as a "convecton") surrounded by almost stationary fluid, or, conversely, a single column of concentrated magnetic flux surrounded by convection cells. Similar localised solutions can be found when convection is oscillatory. In three dimensions, these states are unstable and the behaviour is usually time-dependent, but localisation can still occur.