This tutorial surveys the state of the art in executing discrete event simulation programs on parallel computers, focusing on asynchronous simulation programs where events occur at different points in time. The paper discusses the challenges of parallel discrete event simulation (PDES) and reviews several simulation strategies, including conservative and optimistic approaches. Conservative methods aim to avoid causality errors by determining when it is safe to process an event, while optimistic methods detect and recover from causality errors. The paper critiques existing approaches, highlighting their strengths and weaknesses. It also explores techniques such as deadlock avoidance, deadlock detection and recovery, synchronous operation, time windows, lookahead, conditional knowledge, and optimistic mechanisms like Time Warp. The performance of these methods is evaluated, and their limitations are discussed, particularly the need for static configurations and the overhead of state saving in optimistic systems.This tutorial surveys the state of the art in executing discrete event simulation programs on parallel computers, focusing on asynchronous simulation programs where events occur at different points in time. The paper discusses the challenges of parallel discrete event simulation (PDES) and reviews several simulation strategies, including conservative and optimistic approaches. Conservative methods aim to avoid causality errors by determining when it is safe to process an event, while optimistic methods detect and recover from causality errors. The paper critiques existing approaches, highlighting their strengths and weaknesses. It also explores techniques such as deadlock avoidance, deadlock detection and recovery, synchronous operation, time windows, lookahead, conditional knowledge, and optimistic mechanisms like Time Warp. The performance of these methods is evaluated, and their limitations are discussed, particularly the need for static configurations and the overhead of state saving in optimistic systems.