Parallel processing has seen incredible growth with increasingly complex scientific & engg applications coming to their realm.Task scheduling,a key issue for its success,& design of efficient algorithms play a crucial role in it.Due to NP-completeness of the problem research efforts are mainly focussed at heuristic-based approaches to generate near-optimal schedules within reasonable time & resource constraints.Most of the heuristics, however, ignore practical aspect and/or compromise too much on complexity or performance.This monograph provides an in-depth insight into these issues.An overview of state-of-the-art scheduling,reflecting changing paradigms,is also provided.In addition,for scheduling DAG structured applications,3 efficient algorithms are presented & analyzed for homogeneous, heterogeneous & mixed-parallel computing environments.Selective-duplication heuristic is introduced and its usefulness in dealing with IPC overhead is shown in comparison to list,clustering and duplication-based heuristics.An A-cube performance model is suggested to comprehensively study behavior of algorithm, application & architecture in heterogeneous environment.