This review discusses one-dimensional supramolecular polymers that form in aqueous media. First, naturally occurring supramolecular polymers are described, in particular, amyloid fibrils, actin filaments, and microtubules. Their structural, thermodynamic, kinetic, and nanomechanical properties are highlighted, as well as their importance for the advancement of biologically inspired supramolecular polymer materials. Second, five classes of synthetic supramolecular polymers are described: systems based on (1) hydrogen-bond motifs, (2) large pi-conjugated surfaces, (3) host guest interactions, (4) peptides, and (5) DNA. We focus on recent studies that address key challenges in the field, providing mechanistic understanding, rational polymer design, important functionality, robustness, or unusual thermodynamic and kinetic properties.