Fluid motion driven by thermal gradients is a common and important phenomenon in nature.
It is a major feature of the dynamics of oceans, atmospheres, the interior of stars and planets and in many industrial processes. In a spatially extended system, convection can be initiated by applying a sufficiently steep temperature gradient across a fluid layer. Spatial variations in such convective structures are referred to as patterns. In this talk we will discuss how the physical process of convection can be mathematically modelled and describe the mathematical analysis of patterns, and their defects, which arise in these models.