Valves having seats and counterseats with various contours are provided. In one embodiment, a valve includes a body and a flow control assembly inside the body. The flow control assembly includes a ball, a seat installed on the ball, and a counterseat. The ball is rotatable between open and closed positions to control flow through the body and the seat and counterseat include mating surfaces that engage when the ball is in the closed position such that the seat seals against the counterseat along the mating surfaces. Further, the mating surface of the counterseat can be a concave surface, the mating surface of the seat can be a convex surface, and at least one of the mating surfaces can have a toroidal contour.