Carbon quantum dots (CQDs)/carbon nanodots are a new class of fluorescent carbon nanomaterials having an approximate size in the range of 2–10 nm. The majority of the reported review articles have discussed about the development of the CQDs (via simple and cost-effective synthesis methods) for use in bio-imaging and chemical-/biological-sensing applications. However, there is a severe lack of consolidated studies on the recently developed CQDs (especially doped/co-doped) that are utilized in different areas of application. Hence, in this review, we have extensively discussed about the recent development in doped and co-doped CQDs (using elements/heteroatoms—e.g., boron (B), fluorine (F), nitrogen (N), sulphur (S), and phosphorous (P)), along with their synthesis method, reaction conditions, and/or quantum yield (QY), and their emerging multi-potential applications including electrical/electronics (such as light emitting diode (LED) and solar cells), fluorescent ink for anti-counterfeiting, optical sensors (for detection of metal ions, drugs, and pesticides/fungicides), gene delivery, and temperature probing.