This thesis investigates the uniqueness and asymptotic behavior of tangent flows arising in mean curvature flow, where singularities naturally develop over time. It establishes quantitative estimates that describe the rate of convergence to singularity models and proves a unique continuation property near compact multiplicity-one singularities. The work further extends these results to zero-Maslov Lagrangian mean curvature flows in C², showing that tangent flows are unique even in the presence of higher multiplicity cones. These results provide a unified framework for understanding singularity formation in both classical and Lagrangian settings.