Apparatus and methods for autonomously controlling fluid flow in a subterranean well are presented, and in particular for providing a fluid diode to create a relatively high resistance to fluid flow in one direction and a relatively low resistance to fluid flowing in the opposite direction. The diode is positioned in a fluid passageway and has opposing high resistance and low resistance entries. In one embodiment, the high resistance entry has a concave, annular surface surrounding an orifice and the low resistance entry has a substantially conical surface. The concave, annular surface of the high resistance entry preferably extends longitudinally beyond the plane of the orifice. In a preferred embodiment, the fluid will flow in eddies adjacent the concave, annular surface.