It has been 10 yr since the initial discovery of 'Ultra-Diffuse Galaxies' (UDGs) in the Coma cluster and the revelation that large, low surface brightness galaxies may constitute a greater fraction of galaxies than first thought. This left an open question: Are UDGs something special, or just an extension of the previously known dwarf galaxy population? Seeking to answer this question, in the decade following, dedicated simulations have studied and proposed a myriad of formation pathways to create UDGs. Observations have then pushed the limits of world-class observatories to perform detailed studies of these galaxies in large numbers across the full range of environments in the local Universe. These observations stress test simulations and challenge previous galaxy formation wisdom, with UDGs posing many open puzzles beyond just their unknown formation mechanism. To provide a few pertinent examples: there is observational evidence that not all UDGs follow the standard stellar mass ─ halo mass relationship; there is evidence for UDGs with extraordinarily high levels of alpha enhancement; and there is evidence that some UDGs are much more globular cluster rich than other dwarfs of similar stellar mass. In this Dawes review, we undertake the task of summarising the decade of science since the discovery of UDGs. We focus on the quiescent population of UDGs and review their general properties, their proposed formation scenarios, their internal properties and their globular cluster systems. We also provide a brief conjecture on some future directions for the next decade of UDG research.