Traditionally our understanding of the vast array of different phases of matter has largely been based on symmetry principles. However, in recent years, it’s been realized that there are many phases that lie outside this conventional narrative. The concept of “topological order” has proven to be a particularly exciting new paradigm in this regard, defying the traditional symmetry-based classification of matter and providing a host of strange and exotic phenomena. A vibrant and active field of current research, it continues to draw together a diverse range of ideas from condensed matter, quantum information, high-energy physics and pure mathematics. I will introduce a simple model that contains much of the essential physics of topological order and then discuss the field more broadly, including a taste of some of my own research.