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Mean curvature flow, the gradient flow of the area functional, is the most natural geometric heat flow for embedded hypersurfaces. Being non linear, the flow develops singularities, at which it stops being smooth. One fundamental, often delicate, question for such non linear flows is that of backwards uniqueness. In this talk I will discuss recent backwards uniqueness results, obtained jointly with Josh Daniels-Holgate, which can address some singularities. I will also compare these results to (commonly more robust) forward uniqueness results, and also to the situation in  other equations.