Rigid electromagnetic actuators serve our society in a myriad of ways for more than 200 years. However, their bulky nature restricts close collaboration with humans. Here, we introduce soft electromagnetic actuators (SEMAs) by replacing solid metal coils with liquid-metal channels embedded in elastomeric shells. We demonstrate human-friendly, simple, stretchable, fast, durable, and programmable centimeter-scale SEMAs that drive a soft shark, interact with everyday objects, or rapidly mix a dye with water. A multicoil flower SEMA with individually controlled petals blooms or closes within tens of milliseconds, and a cubic SEMA performs programmed, arbitrary motion sequences. We develop a numerical model supporting design and opening potential routes toward miniaturization, reduction of power consumption, and increase in mechanical efficiency. SEMAs are electrically controlled shape-morphing systems that are potentially empowering future applications from soft grippers to minimally invasive medicine.