Understanding turbulence in magnetically confined fusion plasmas is an important issue on the long road to fusion energy as a power source for humanity. Fusion plasmas are extreme, strongly driven systems, far from thermodynamic equilibrium, in which turbulence plays a major role. This book reviews some of the observations that reveal the complex nature of plasma turbulence in detail and explains their implications. The change in paradigm needed to understand the observations is then discussed and mathematical models are highlighted that might address the dynamics better than traditional models. Along the way, a range of advanced analysis tools needed to characterize turbulence in this complex regime are presented and illustrated, including non-linear analyses, causality, and intermittence. The book aims to stimulate their broader adoption for the analysis of data from both experiments and numerical turbulence simulations. Part of IOP Series in Plasma Physics.