Carbon quantum dots (CQDs) have emerged in the research of optoelectronic devices as a kind of novel photoelectronic materials in recent years because of their excellent properties such as high fluorescence quantum yield, tunable bandgap, good solvent dispersion, high electron transporting performance, long hot-electron lifetime, wide optical absorption, low cost and environmental friendliness. In this paper, their synthesis, optoelectronic properties, applications and existed problems were reviewed, which will provide reference for expanding the application of CQDs in lighting, display, communication and solar cells in the future. Firstly, the synthesis, structure and optical properties of CQDs were summarized, and the emission mechanisms of CQDs from quantum confinement effect, surface defects or molecular state were systematically investigated. The CQD emission from surface defects can cause non-radiative transition, reducing the fluorescence quantum yield (QY) of CQDs. Therefore, in order to improve the electroluminescence and photoluminescence properties of CQDs, the non-radiative transition caused by surface defects should be avoided as far as possible. As for the emission of CQDs from molecular state, with the increasing of reaction temperatures, the luminescent groups of molecular state gradually are carbonized and the carbon cores of CQDs gradually are formed, the proportion of luminescence from molecular state gradually decreases while carbon cores gradually dominate the emission of CQDs. In addition, the heteroatom doping can significantly adjust the bandgap and electron cloud density of CQDs, resulting in the improvement of their QY. The impact of their particle size, structure and surface state on the emission wavelengths of CQDs were summarized. The bandgap width of CQDs gradually decrease with the increasing the particle size, sp2 conjugation degree and oxygen-containing functional groups of CQDs, which help their emission with long wavelengths. The solid-state luminescence property of CQDs is necessary for the application of CQDs in solid state lighting and full color display. However, in most cases, the CQDs in solid-state suffer obvious fluorescence quenching, which inevitably reduces the performance of optoelectronic devices. Increasing the interparticle spacing of CQDs is an effective measure for suppressing the solid-state fluorescence quenching through dispersing CQDs in a bulk matrix or long-chain passivation. Secondly, the recent developments of CQD application in optoelectronic devices including white light-emitting diode (WLED), quantum dot-based electroluminescent light-emitting diode (QLED), laser diode (LD), visible light communication (VLC) and polymer solar cell (PSC) were introduced. The emission wavelength of CQDs has been extended from deep-ultraviolet to near-infrared region, and the QY of blue, green and red emission CQDs has reached more than 80%. Moreover, the CQDs with narrow bandwidth emission were obtained, which endows CQDs with the broad application prospects in the field of LED and LD as photoluminescence phosphor powders and electroluminescence emitting layers. Owing to the excellent photoluminescence properties and short fluorescence lifetime of CQDs, they also have potential applications in VLC as photoluminescence phosphor powders. In addition, owing to their excellent electron transporting abilities and solution processability, they also can be used as electron acceptor or electron transport layer in PSC. Finally, the major problems and opportunities for CQDs in optoelectronic were analyzed and outlined. Their solid-state luminescent quenching, long-wavelength emission, high QY and thermal stability and product yield of CQDs need to be improved in the future.