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Physical guidance from the underlying matrix is a key regulator of cancer invasion and metastasis. We explore the effects of surface topography on the migration phenotype of multiple breast cancer cell lines using aligned nanoscale ridges and asymmetric sawtooth structures. Both benign and metastatic breast cancer cells preferentially move parallel to nanoridges, with enhanced speeds compared to flat surfaces. In contrast, asymmetric sawtooth structures unidirectionally bias the movement of breast cancer cells in a cell-type-dependent manner. Quantitative analysis shows that the level of bias in cell migration increases when cells move with higher speeds or with higher directional persistence. Live-cell imaging studies further reveal that actin polymerization waves are unidirectionally guided by the sawteeth in the same direction as the cell motion. High-resolution fluorescence imaging and scanning electron microscopy studies reveal that two breast cancer cell lines with opposite migrational profiles exhibit profoundly different cell cortical plasticity and focal adhesion patterns. These results suggest that the overall migration response of cancer cells to surface topography is directly related to the underlying cytoskeletal architectures and dynamics, which are regulated by both intrinsic and extrinsic factors.