Frequent rise of interval-censored time-to-event data in randomized clinical trials (e.g., progression-free survival [PFS] in oncology) challenges statistical researchers in the pharmaceutical industry in various ways. These challenges exist in both trial design and data analysis. Conventional statistical methods treating intervals as fixed points, which are generally practiced by pharmaceutical industry, sometimes yield inferior or even flawed analysis results in extreme cases for interval-censored data. In this article, we examine the limitation of these standard methods under typical clinical trial settings and further review and compare several existing nonparametric likelihood-based methods for interval-censored data, methods that are more sophisticated but robust. Trial design issues involved with interval-censored data comprise another topic to be explored in this article. Unlike right-censored survival data, expected sample size or power for a trial with interval-censored data relies heavily on the parametric distribution of the baseline survival function as well as the frequency of assessments. There can be substantial power loss in trials with interval-censored data if the assessments are very infrequent. Such an additional dependency controverts many fundamental assumptions and principles in conventional survival trial designs, especially the group sequential design (e.g., the concept of information fraction). In this article, we discuss these fundamental changes and available tools to work around their impacts. Although progression-free survival is often used as a discussion point in the article, the general conclusions are equally applicable to other interval-censored time-to-event endpoints.