Complex coacervation is an associative, liquid-liquid phase separation that can 
occur in solutions of oppositely-charged macromolecular species, such as 
proteins, polymers, and colloids. This process results in a coacervate phase, 
which is a dense mix of the oppositely-charged components, and a supernatant 
phase, which is primarily devoid of these same species. First observed almost a 
century ago, coacervates have since found relevance in a wide range of 
applications; they are used in personal care and food products, cutting edge 
biotechnology, and as a motif for materials design and self-assembly. There has 
recently been a renaissance in our understanding of this important class of 
material phenomena, bringing the science of coacervation to the forefront of 
polymer and colloid science, biophysics, and industrial materials design. In 
this review, we describe the emergence of a number of these new research 
directions, specifically in the context of polymer-polymer complex coacervates, 
which are inspired by a number of key physical and chemical insights and driven 
by a diverse range of experimental, theoretical, and computational approaches.