Implantable shunt devices and methods for draining cerebrospinal fluid from a patient's subarachnoid space include a shunt having opposed first and second ends, the second end being constructed to penetrate a wall of a sigmoid, transverse, straight, or sagittal sinus of the patient, a one-way valve, a hollow passageway extending between the second end and the one-way valve such that cerebrospinal fluid can be drained through the second end and out through the valve, and a mechanism coupled to the shunt and configured to anchor the shunt at a desired location proximal to the subarachnoid space.