Brazing is a 5000-year-old joining process which still meets advanced joining challenges today. In brazing, components are joined by heating above the melting point of a filler metal placed between them; on solidification a joint is formed. It provides unique advantages over other joining methods, including the ability to join dissimilar material combinations (including metal-ceramic joints), with limited microstructural evolution; producing joints of relatively high strength which are often electrically and thermally conductive. Current interest in brazing is widespread with filler metal development key to enabling a range of future technologies including; fusion energy, Solid Oxide Fuel Cells and nanoelectronics, whilst also assisting the advancement of established fields, such as automotive lightweighting, by tackling the challenges associated with joining aluminium to steels. This review discusses the theory and practice of brazing, with particular reference to filler metals, and covers progress in, and opportunities for, advanced filler metal development.