The Log-rank test and Cox Proportional hazards model are often the default analysis choices for the between-group comparisons of time-to-event data. The optimal property and robustness of these methods are well established under certain regular conditions, with which the methods are arguably considered as the "gold standard" for survival analysis. It is of interest to understand the performance and feasibility of them under "not-so-regular" conditions. In this presentation we use graphical tools to conduct a 360 degree review of the methods under a wide variety of data situations, including 1) various types of representative non-proportional hazards, 2) various types of censorings, 3) extreme data conditions, 4) mixture distribution, and 5) joint modeling. The design and analysis of clinical trials in subjects with non-muscle invasive bladder cancer of carcinoma in situ (CIS) is provided as an example to illustrate the practical considerations summarized from the review.