Abstract: Interval-censored failure time data are a general type of failure time or time-to-event data where the failure time of interest is known or observed only to lie in an interval or window instead of being observed exactly. They often occur in many fields, including demographical studies, epidemiological studies, medical or public health research and social science, and in different forms. A common and general set-up that naturally yields interval-censored data is the study with longitudinal or periodical follow-ups such as many clinical trials or observation studies. In this paper, after some brief discussion about the background and some commonly used models, we will review some recent advances, mainly during about last five years, on several important topics related to regression analysis as well as some issues that need more research in the analysis of interval-censored data.