Machines for bending profiles, metal sheets and the like are provided. Such machines include those having a structure or frame and a bending device with three rollers. The axis (x1) of the first roller is fixed relative to the structure or frame, while the axes (x2, x3) of the second and third rollers are movable relative to each other, and hence each relative to the axis (x1) of the first roller, so as to define a curved path with an adjustable radius of curvature along which the material to be bent is caused to move passing between said rollers. The bending device may further include an adjustment mechanism for adjusting the position of the axes (x2, x3) of the second and third rollers with two degrees of freedom. The adjustment mechanism may include a pair of tilting arms hinged to the structure or frame so as to tilt about respective fixed axes of rotation (x4, x5) oriented parallel to the axes (x1, x2, x3) of the three rollers. The axes (x2, x3) of the second and third rollers may be guided each by a respective tilting arm along a respective direction of translation (y1, y2) which is fixed relative to that tilting arm.