A guidewire or a catheter for crossing vascular occlusions comprises a shaft having a proximal end and a distal end, and a drive member having a proximal and a distal end, the drive member being rotatably disposed within and along a longitudinal axis of the guidewire shaft. An actuator is connected to the proximal end of the drive member, the actuator imparting a rotation to the drive member. An asymmetrical rotating tip is attached to the distal end of the drive member and driven in rotation about the longitudinal axis of the shaft by the drive member. The rotating tip may include a protruding portion that projects from a plane defined by an outer surface of the guidewire shaft to render the rotating tip asymmetrical with respect to the longitudinal axis of the shaft. The protruding portion creates a volume of revolution as the asymmetrical tip rotates, which facilitates crossing a vascular occlusion by displacing and exerting pressure on stenotic material causing the occlusion. Alternatively, the rotating tip may be symmetrical. A coupling member may be attached to the distal end of the shaft and may include a distal angled surface. When the tip includes a mating angled surface, rotation of the drive member causes the tip to undergo both a reciprocal and a rotational motion along and about the longitudinal axis of the shaft.