In polycrystals, the interaction of dislocations and twins with grain boundaries (GBs) plays a role in hardening and formability during plastic deformation. While dislocation-GB interactions are relatively well-understood, twin-GB interactions remain mostly unknown. Here, an approach using molecular dynamics and phase-field simulations is followed to study the forward and lateral interactions between {101¯2} twins and tilt grain boundaries in Mg. Molecular dynamics results show that the resolved shear stress on slip/twinning modes of the neighboring grain, not the geometric alignment, is the dominant factor in determining the outcome of the twin-GB interactions. For some lateral interaction configurations, as the misorientation angle increases, the resolved shear stress on the same {101¯2} twin variant of the neighboring grain reduces while it increases for slip or I2 stacking fault emissions or other twin modes such as {112¯1} and {101¯1}, explaining why twin transmission is not seen at high misorientation angles. Furthermore, lateral and forward interactions of the twin with tilt grain boundaries whose misorientation axes are normal to the coherent twin boundary show significantly different outcomes. For the forward interaction, the twin is absorbed and stacking faults are emitted when interacting for low misorientation angles (up to 30°) while the lateral interaction results in twin transmission, nucleation of a {112¯1} twin, and emission of I2 stacking faults. Finally, comparisons between twin interactions with symmetric and asymmetric tilt GBs with different GB structures show similar outcomes.