Title: On Label Shift in Domain Adaptation via Wasserstein Distance. Abstract: We study the label shift problem between the source and target domains in general domain adaptation (DA) settings.  We consider transformations transporting the target to source domains, which enable us to align the source and target examples.   Through those transformations,  we define the label shift between two domains via optimal transport and develop the theory to investigate the properties of DA under various DA settings (e.g., closed-set, partial-set, open-set, and universal settings).  Inspired from the developed theory, we propose Label and Data Shift Reduction via Optimal Transport (LDROT) which can mitigate the data and label shifts simultaneously.  Finally, we conduct comprehensive experiments to verify9our theoretical findings and compare LDROT with state-of-the-art baselines.