Space-time finite elements are a compelling approach for solving transient partial differential equations. By employing finite element trial function spaces in both space and time, local refinement in time is admitted. In particular, simplex space-time meshes extend the flexibility of unstructured spatial meshes to the temporal dimension [1]. With semi-discrete time discretization schemes, moving domains or moving features in the solution field are challenging to treat alongside adaptive mesh refinement, due to the need for robust mesh update procedures and, in the case of entire remeshing, accurate solution transfer between meshes. In contrast, an adaptive space-time discretization addresses both aspects within a unified framework. In this work, we investigate the use of established a posteriori error estimation techniques—commonly developed for conventional spatial meshes—within time-continuous space-time formulations [2]. Remaining in the unstructured mesh paradigm, we assess how standard simplex mesh generation and adaptation methods can be leveraged to resolve small-scale features in space and in time. For this purpose, anisotropic meshing capabilities enable element sizes to vary independently in space and time, allowing for precisely targeted enrichment of the approximation space to lower computational cost compared to isotropic meshes. We apply the refinement strategies to benchmark problems and compare accuracy and efficiency against globally refined meshes and manually prescribed refinement patterns. We also evaluate the practicality and performance of the adaptive scheme within a highly parallel finite element framework. [1] M. von Danwitz, V. Karyofylli, N. Hosters, and M. Behr. Simplex space-time meshes in compressible flow simulations. Int. J. Numer. Methods Fluids., 2019. [2] J. P. De S. R. Gago, D. W. Kelly, O. C. Zienkiewicz, I. Babuska. A posteriori error analysis and adaptive processes in the finite element method: Part ii—adaptive mesh refinement. Int. J. Numer. Mech. Eng., 1983.