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In this talk, we will study the mean curvature flow in R^3.  The extrinsic diameter is trivially bounded by the avoidance principle, but the intrinsic diameter is far subtler: near singularities, the evolving surface may develop long, spiraling, or fractal-like regions whose intrinsic geometry could, a priori, degenerate. We show that the intrinsic diameter of mean curvature flow in R^3 is uniformly bounded as one approaches the first singular time, which confirms a conjecture of Haslhofer. In addition, we establish several sharp quantitative estimates of mean curvature flow. This is a joint work with Yiqi Huang(MIT).