Methods and tools for forming contoured composite structures are disclosed. Methods include positioning a sheet of composite material relative to a structure of shape memory alloy, heating the structure of shape memory alloy to deform the structure of shape memory alloy to a deformed conformation and thereby conform the sheet of composite material to a desired contour corresponding to the deformed conformation of the structure of shape memory alloy. Tools include a structure of shape memory alloy and a heat source for heating the structure of shape memory alloy to conform a sheet of composite material to a desired contour corresponding to the deformed conformation of the structure of shape memory alloy.