Time-to-event endpoints are typically used as primary or key secondary endpoints in registration oncology and hematology trials. Non-proportional hazards present frequently in oncology and hematology trials due to many reasons and/or different mechanism of actions of the drugs. For example, survival curves in randomized immunotherapy trials can show a delayed separation between treatments, and this implies non-proportional hazards of the survival curves. In this presentation, we present several case studies of the oncology and hematology trials that non-proportional hazards are observed. We will show simulation results and also examine and compare methods for evaluating efficacy when non-proportional hazards present.