Abstract: In 2D topological phases with symmetry, the fractional excitations in the system can transform under symmetry in a fractional way, e.g. by carrying fractional symmetry charges. With different types of topological order and different symmetries, what symmetry fractionalization (SF) patterns are possible in general? This question becomes particularly interesting with recent experimental progress towards realizing spin liquids and we try to answer this question in this talk. In particular, we point out that some seemingly consistent SF patterns are actually anomalous, i.e. they cannot be realized in purely 2D systems. To exclude these cases, we discuss two anomaly detection methods: the flux threading method, which is physically intuitive but applies only to special cases, and the gauging obstruction method, which is mathematically complete and straight-forward to apply. We give specific examples of anomalous SF patterns to be detected by these methods and discuss the interesting possibility of realizing them on the surface of 3D systems.