The creation of a generic and modular query optimization and processing infrastructure can provide significant benefits to XML data management. Key pieces of such an infrastructure are the physical operators that are available to the execution engine, to turn queries into execution plans. Such operators, to be efficient, need to implement sophisticated algorithms for logical XPath or XQuery operations. Moreover, to enable a cost-based optimizer to choose among them correctly, it is also necessary to provide cost models for such operator implementations. In this paper we present two novel families of algorithms for XPath physical operators, called LookUp (LU) and Sort-Merge-based (SM), along with detailed cost models. Our algorithms have significantly better performance compared to existing techniques over any one of a variety of different XML storage systems that provide a set of common primitive access methods. To substantiate the robustness and efficiency of our physical operators, ...