© 2016 IOP Publishing Ltd. Emission of terahertz (THz) electromagnetic (EM) waves from a high critical temperature (T c) superconductor intrinsic Josephson junction (IJJ) is a new and promising candidate for practical applications of superconducting devices. From the engineering viewpoint, the IJJ THz source is competitive against the present semiconducting THz sources such as quantum cascade lasers (QCLs) and resonance tunnelling diode oscillators because of its broad tunable frequency range and ease of the fabrication process for the device. The emitted EM waves are considered to be coherent because the emission is yielded by synchronisation of thousand stacked IJJs consisting of the mesa device. This synchronisation is peculiar: the resonant frequency of each IJJ is distributed because the cross section of the mesa device is trapezoidal in shape. One of the key features of the synchronisation mechanism is the temperature inhomogeneity of the emitting device. In this topical review, we describe the recent progress in studies of IJJ THz sources with particular emphasis on the relevance of the temperature inhomogeneity to the synchronisation and the emission intensity. This review is of specific interest because the IJJ THz source shows the rich variety of functions due to self-heating which has always been a detrimental feature in the present superconducting devices. Moreover, the thermal managements used for IJJ THz sources will be common with those of other semiconducting devices such as QCLs. In addition, this review is to invite the readers into related research through the detailed descriptions of experimental procedures.