Lithium niobate on insulator (LNOI) was regarded as a competitive integrated optical platform due to the excellent optical performance of lithium niobate crystal and integration characteristics of thin-film devices. In addition to the research on transmission and control devices, such as waveguides and modulators, significant progress has been made in LNOI lasers recently. The research status of the rapidly developing LNOI microcavity laser was reviewed in this paper. Firstly, the main technical schemes of rare-earth ion doping of bulk lithium niobate and LNOI, as well as the recent exploration on the preparation of rare-earth ion doped LNOI micro-/nano- optical devices, were introduced; Secondly, the research progresses on Erbium-doped lithium niobate on insulator (Er-LNOI) microdisk and microring cavity lasers were summarized; Then, the working mechanism of several common methods to realize single-mode laser in microcavity laser system were described. The research progresses on Er-LNOI single-mode lasers utilizing "Vernier effect" and mode-loss modulation were introduced in the following; Finally, based on the reported research results of LNOI lasers, the limitations of the current research and the future research directions were discussed.