Commonly encountered problems in the manipulation of objects with robotic hands are the contact force control and the setting of approaching motion. Microelectromechanical systems (MEMS) sensors on robots offer several solutions to these problems along with new capabilities. In this review, we analyze tactile, force and/or pressure sensors produced by MEMS technologies including off-the-shelf products such as MEMS barometric sensors. Alone or in conjunction with other sensors, MEMS platforms are considered very promising for robots to detect the contact forces, slippage and the distance to the objects for effective dexterous manipulation. We briefly reviewed several sensing mechanisms and principles, such as capacitive, resistive, piezoresistive and triboelectric, combined with new flexible materials technologies including polymers processing and MEMS-embedded textiles for flexible and snake robots. We demonstrated that without taking up extra space and at the same time remaining lightweight, several MEMS sensors can be integrated into robotic hands to simulate human fingers, gripping, hardness and stiffness sensations. MEMS have high potential of enabling new generation microactuators, microsensors, micro miniature motion-systems (e.g., microrobots) that will be indispensable for health, security, safety and environmental protection.