Decayless transverse kink oscillations of solar coronal loops (or decayless oscillations for short) have attracted great attention since their discovery. In contrast to the previously reported decaying kink oscillations, they are not associated with any external impulsive events and are found to show no obvious decay of amplitude. Besides, their ubiquitous existence suggests that they might play an important role in the process of coronal heating and diagnostics of the properties of coronal loops. In this review, we summarize the research progress of decayless oscillations. The observational results include their amplitude, period, scaling rules, polarization and multiple harmonics. We also introduce different types of theoretical models on their generation mechanisms. Moreover, we also give some examples of their application in coronal seismology. In the last section of this review, we discuss future perspectives on the research of decayless oscillations.