Low profile valves are described. In an embodiment, a tubular member for fluid transport has a valve constructed within a wall of the tubular member for controlling a radial flow of fluid, such as water, oil, or gas, through the wall without impeding the flow of fluid or tools through the tubular member or near the exterior of the tubular member. The low profile valve may be used, for example, in the oil and gas industries as a pressure relief valve or check valve. When used as a pressure relief valve, a load member such as a spring, strap, or rocker arm maintains a backpressure on the valve. Example low profile valves can provide flow control from within a very thin annulus between other components.