Carbon dots (CDs) - small crystalline or amorphous carbon-based nanoparticles - have attracted much attention as promising fluorescent materials for a wide range of applications. One of their widely accepted advantages is the simplicity of the formation of highly luminescent CDs from a wide variety of organic precursors. At the same time, several recent studies on these chemically synthesized CDs raised questions about the nature of the resulting products. Their strong fluorescence can arise due to the presence of molecular organic fluorophores, not necessary CDs, as was assumed in the earlier publications. In this review, we consider fundamental characteristics of CDs and discuss several issues that currently prevent a better understanding of their structure-property correlation. Analysis of recent related studies identifying the presence of organic fluorophores in CDs with an emphasis on the optical properties of the synthesis products shows that their emission characteristics may be a complex interplay of stand-alone molecular fluorophores and their aggregates, possibly embedded in an amorphous carbon/polymer network. The review concludes with an outlook towards the challenges in the field of the bottom-up synthesized CDs, and their proper identification within the variety of the organic side-products eventually formed during the synthesis. (C) 2018 Elsevier Ltd. All rights reserved.