The invention concerns a bend stiffener (10, 32) for locally protecting an elongate flexible member (14) from excessive curvature when the elongate flexible member is deployed in water. The bend stiffener comprises an elongate stiffener body (34) which has a root end, a free end, and a passage (36) extending through the stiffener body from the root end to the free end for receiving and embracing the flexible member. A coupling (16) at or toward the root end of the stiffener body serves to mount the stiffener body. The stiffener body is sufficiently flexible to curve somewhat along with the flexible member when the flexible member suffers a bending load and carries a sensor module which is located proximate the free end of the bend stiffener and is configured to sense inclination and/or orientation and/or movement of the free end of the bend stiffener.