Abstract: Multiprocessor is very common in embedded computing systems because it can meet the performance, cost and energy/power consumption goals. Multiprocessor system-on-chip is often heterogeneous multiprocessors and integrates multiple instruction-set processors on a single chip that implements most of the functionality of a complex electronic system. Current trends indicate that multiprocessor system-on-chip is being increasingly used in application such as image processing, network multimedia, embedded system, and so on. Scheduling and mapping of tasks are important key problems in multiprocessor system-on-chip design, and are substantially more difficult than scheduling a uniprocessor. The basic architecture and design challenge of multiprocessor system-on-chip task scheduling algorithm are introduced. In particular, the current research progresses are summarized according to scheduling algorithm analysis and implementation framework. The scheduling algorithm analysis is classified into three categories, and scheduler implementation framework is classified into two categories by using task modeling. Many open research problems are pointed out. Because of the large variety of timeliness requirements in real-time applications, an important goal is to find canonical representations of task considering timing constraints. It is an important target to implement high-effects scheduler based on multiprocessor system-on-chip platform. By comparing and analyzing these different projects and algorithms, researchers of related topic can gain useful information about task scheduling problem.