Extended Reality (XR) is an emerging technology spanning diverse application domains and offering immersive user experiences. However, its unique characteristics, such as six degrees of freedom interactions, present significant testing challenges distinct from traditional 2D GUI applications, demanding novel testing techniques to build high-quality XR applications. This paper presents the first systematic mapping study on software testing for XR applications. We selected 34 studies focusing on techniques and empirical approaches in XR software testing for detailed examination. The studies are classified and reviewed to address the current research landscape, test facets, and evaluation methodologies in the XR testing domain. Additionally, we provide a repository summarising the mapping study, including datasets and tools referenced in the selected studies, to support future research and practical applications. Our study highlights open challenges in XR testing and proposes actionable future research directions to address the gaps and advance the field of XR software testing.