Systems and methods are provided herein that generally involve shunting fluid, e.g., shunting cerebrospinal fluid in the treatment of hydrocephalus. Self-cleaning catheters are provided which include split tips configured such that pulsatile flow of fluid in a cavity in which the catheter is inserted can cause the tips to strike one another and thereby clear obstructions. Catheters with built-in flow indicators are also provided. Exemplary flow indicators include projections that extend radially inward from the interior surface of the catheter and which include imageable portions (e.g., portions which are visible under magnetic resonance imaging (MRI)). Movement of the flow indicators caused by fluid flowing through the catheter can be detected using MRI, thereby providing a reliable indication as to whether the catheter is partially or completely blocked.