The study of anthropogenic climate change presents a range of fundamental challenges for scientific and wider academic inquiry. The nature and implications of these challenges are often not well appreciated. In this talk I will present seven key characteristics that frame the study of climate change in both the sciences and the social sciences. I will begin by discussing what we mean by the term “climate” and why traditional interpretations of the term are ill-suited to the study of climate change in the 21st century. Building on this I will present the seven characteristics with a particular focus on the consequences of nonlinearity. Each one is already the subject of widespread investigation but the context of anthropogenic climate change transforms issues that in different situations are perhaps soluble into ones which represent deep conceptual challenges. I will conclude with a discussion of more and less valuable ways to move forward in this field which is of such critical importance for society.