The objective of this paper is to present a systematic review of existing sensor-based control methodologies for applications that involve direct interaction between humans and robots, in the form of either physical collaboration or safe coexistence. To this end, we first introduce the basic formulation of the sensor-servo problem, then present the most common approaches: vision-based, touch-based, audio-based, and distance-based control. Afterwards, we discuss and formalize the methods that integrate heterogeneous sensors at the control level. The surveyed body of literature is classified according to the type of sensor, to the way multiple measurements are combined, and to the target objectives and applications. Finally, we discuss open problems, potential applications, and future research directions.