Polymeric materials, which include plastics, fabrics and the vast majority of biological substances, are abundant in modern society. On the molecular scale, these materials are built from the interconnection of similar chemical subunits to form chainlike macromolecules. The medical, electrochemical, synthetic and materials science communities have increasingly turned their attention to polyelectrolytes, a subset of polymers with electric charge, in part because of their ability to spontaneously and reversibly phase-separate (complex) in aqueous solution. This entropic and electrostatic separation can yield well-defined nanoparticles, dynamic gels and other useful materials. These materials are called polyelectrolyte complexes (PECs) and have formed the basis of complex-core micelle technologies that show promise as nanoscale drug-delivery vehicles for cancer treatment, and which have long been suspected to play a role in the chemical origin of life. This article describes the thermodynamics underlying polyelectrolyte complexation, and then illustrates the application of PECs in medicine and their possible role in the beginning of life, interconnecting these far-flung domains through their reliance on the spontaneous organisation of nanoscale space by chemical activity, the singular physical process of electrolyte complexation.