Carbon dots (CDs) are an emerging family of nanosystems displaying a range of fascinating properties. Broadly speaking, they can be described as small, surface-functionalized carbonaceous nanoparticles characterized by an intense and tunable fluorescence, a marked sensitivity to the environment and a range of interesting photochemical properties. CDs are currently the subject of very intense research, motivated by their possible applications in many fields, including bioimaging, solar energy harvesting, nanosensing, light-emitting devices and photocatalyis. This review covers the latest advancements in the field of CDs, with a focus on the fundamental understanding of their key photophysical behaviour, which is still very debated. The photoluminescence mechanism, the origin of their peculiar fluorescence tunability, and their photo-chemical interactions with coupled systems are discussed in light of the latest developments in the field, such as the most recent results obtained by femtosecond time-resolved experiments, which have led to important steps forward in the fundamental understanding of CDs. The optical response of CDs appears to stem from a very complex interplay between the electronic states related to the core structure and those introduced by surface functionalization. In addition, the structure of CD energy levels and the electronic dynamics triggered by photo-excitation finely depend on the microscopic structure of any specific sub-type of CD. On the other hand, this remarkable variability makes CDs extremely versatile, a key benefit in view of their very wide range of applications.