Cox model inference and the log-rank test have been the cornerstones for design and analysis of clinical trials with survival outcomes. We summarize some recently developed methods for analyzing survival data when the hazards may possibly be non-proportional, and also propose some new estimators for summary measures of the treatment effect. Without the proportional hazards assumption, these methods often improve the log-rank test and inference procedures based on the Cox model, as well as non-parametric procedures currently available in the literature. The proposed methods have sound theoretical justifications and can be computed quickly. R codes for implementing them are available. Illustrations with clinical trials are provided.