This review addresses ongoing discussions involving nanolaser experiments, particularly those related to thresholdless lasing or few-emitter devices. A quantum-optical (quantum-mechanical active medium and radiation field) theory is used to examine the emission properties of nanolasers under different experimental configurations. The active medium is treated as inhomogeneously broadened semiconductor quantum dots embedded in a quantum well, where carriers are introduced via current injection.Comparisons are made between a conventional laser and a nanolaser with a spontaneous emission factor of unity, as well as a laser with only a few quantum dots providing the gain. It is found that the combined exploration of intensity, coherence time, photon autocorrelation function and carrier spectral hole burning can provide a unique and consistent picture of nanolasers in the new regimes of laser operation during the transition from thermal to coherent emission. Furthermore, by reducing the number of quantum dots in the optical cavity, a clear indication of non-classical photon statistics is observed before the single-quantum-dot limit is reached. Keywords: nanolasers; optoelectronics; photon statistics; quantum light sources; quantum optics; semiconductor quantum dots; thresholdless lasing FROM CONVENTIONAL TO NANOLASERS Advances in nanofabrication have drastically reduced the size and increased the quality of optical cavities, enabling optical components with dimensions near the diffraction limit. 1-3 Among the driving forces for substantial miniaturization of lasers are technological applications, such as optical interconnects for information processing and communications, where reducing the power consumption is a priority. 4 From a research viewpoint, such efforts are motivated by a new quantum limit that is reachable with nanolasers consisting of a few emitters [5][6][7] or even a single emitter [8][9][10] and low intracavity photon numbers sustained by stimulated emission. 11 Entering the regime of cavity quantum electrodynamics (CQED), nanolasers can provide non-classical light for applications in quantum information. 12 Novel nano-optical structures, such as pillar vertical-cavity surfaceemitting lasers, microdisks, photonic lattices, nanowires and plasmonic resonators, 13-16 enable the extension of optical-mode confinement from one-dimensional to three-dimensional (3D). The features of 3D mode confinement include spectrally widely separated cavity modes, allowing for the possibility of only one mode overlapping with the spontaneous emission spectrum. CQED phenomena include the enhancement 17 or inhibition 18 of spontaneous emission.The spontaneous emission factor b is a quantitative measure of optical resonator control over spontaneous emission. This factor is defined as the spontaneous emission rate into the laser mode divided by the total spontaneous emission rate. For small values of b, which are typical for conventional lasers, the onset of stimulated emission produces a distinct jump in output intensity. Rec...