Spatial transcriptomics (ST) brings new dimensions to the analysis of single-cell data. While some methods for data analysis can be ported over without major modifications, they are the exception rather than the rule. Trajectory inference (TI) methods in particular can suffer from significant challenges due to spatial batch effects in ST data. These can add independent sources of noise to each time point. Pioneering methods for TI on ST data have focused primarily on addressing the batch effects in physical arrangement, i.e., where tissues are deformed in different ways at different time points. However, other challenges arise due to the measurement granularity of ST technologies, as well as a bias from slicing. In this review, we examine the sources of these challenges, and we explore how they are addressed with current state-of-the-art STTI methods. We conclude by highlighting some opportunities for future method development.