In this elementary course, we will introduce some of the 69 documented anomalies of the most complex of liquids —water— focusing on recent progress in understanding these anomalies by combining information provided by recent spectroscopy experiments and simulations on water in bulk, nanoconfined and biological environments. We will interpret evidence from recent experiments designed to test the hypothesis that liquid water has behavior consistent with the hypothesized “liquid polymorphism” in that water might exist in two different phases. We will also discuss recent work on nanoconfined water anomalies as well as the apparently related, and highly unusual, behavior of water in biological environments. Finally, we will discuss how the general concept of liquid polymorphism is proving useful in understanding anomalies in other liquids, such as silicon, silica, and carbon, as well as metallic glasses, which have in common that they are characterized by two characteristic length scales in their interactions.