Fluorescent carbon nanoparticles or carbon quantum dots (CQDs) are a new class of carbon nanomaterials that have emerged recently and have garnered much interest as potential competitors to conventional semiconductor quantum dots. In addition to their comparable optical properties, CQDs have the desired advantages of low toxicity, environmental friendliness low cost and simple synthetic routes. Moreover, surface passivation and functionalization of CQDs allow for the control of their physicochemical properties. Since their discovery, CQDs have found many applications in the fields of chemical sensing, biosensing, bioimaging, nanomedicine, photocatalysis and electrocatalysis. This article reviews the progress in the research and development of CQDs with an emphasis on their synthesis, functionalization and technical applications along with some discussion on challenges and perspectives in this exciting and promising field.