Querying live media streams is a challenging problem that becomes an essential requirement in a growing number of applications. We address the problem of evaluating continuous queries on media streams produced by media sources such as webcams and microphones. The temporal attributes and the order of stream tuples play essential roles in live stream generation and query execution. Furthermore, the temporal constraints and query semantics of related streams provide additional query optimization opportunities. We investigate the modeling issues and introduce the query processing techniques of a live media stream management system (MedSMan), including media capturing, automatic feature generating, declaration and query languages, temporal stream operators and querying algorithms. A prototype is implemented and we present experimental results to show the performance of our prototype using various real-time media experiments.