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Modern weather and climate models share a common heritage, and often even components, however they are used in different ways to answer fundamentally different questions. As such, attempts to emulate them using machine learning should reflect this. While the use of machine learning to emulate weather forecast models is a relatively new endeavour there is a rich history of climate model emulation. This is primarily because while weather modelling is an initial condition problem which intimately depends on the current state of the atmosphere, climate modelling is predominantly a boundary condition problem. In order to emulate the response of the climate to different drivers therefore, representation of the full dynamical evolution of the atmosphere is neither necessary, or in many cases, desirable. Climate scientists are typically interested in different questions also. Indeed emulating the steady-state climate response has been possible for many years and provides significant speed increases that allow solving inverse problems for e.g. parameter estimation. Nevertheless, the large datasets, non-linear relationships and limited training data make Climate a domain which is rich in interesting machine learning challenges. Here I seek to set out the current state of climate model emulation and demonstrate how, despite some challenges, recent advances in machine learning provide new opportunities for creating useful statistical models of the climate.