This is the opening workshop within the programme, Mathematical and Statistical Approaches to Climate Modelling and Prediction. The aim of this conference-style workshop is to bring together expert researchers from the fields of mathematics, statistics and climate science to pose and tackle the major issues confronting climate prediction. The conference will begin by setting out the challenges for improving our understanding and modelling of Earth's climate. Two days of the workshop will be dedicated to fundamental issues of complexity and predictability of Earth's climate as a non-linear system. We will discuss the paradox of spatial (and therefore process) resolution versus replication, and the role of diverse classes of climate model. Day four will focus on the principle of maximum entropy production (MEP) as applied to climate. The final day will concentrate on the toolkit of stochastic physical models as components of ocean-atmosphere climate models. As well improving the representation of physical processes, these sub-grid models can account for structural (epistemological) uncertainty in traditional climate models. The workshop has been organised to encourage maximum participation and discussion between the talks, and thus to kick-start the exchange of ideas for the remaining programme.