Magnetic liquids called ferrofluids have been used in applications ranging from audio speaker cooling and rotary pressure seals to retinal detachment surgery and implantable artificial glaucoma valves. Recently, ferrofluids have been investigated as a material for use in magnetically controllable liquid droplet robotics. Liquid droplet robotics is an emerging technology that aims to apply control theory to manipulate fluid droplets as robotic agents to perform a wide range of tasks. Furthermore, magnetically controlled micro-robotics is another popular area of study where manipulating a magnetic field allows for the control of magnetized micro-robots. Both of these emerging fields have potential for impact toward medical applications: liquid characteristics such as being able to dissolve various compounds, be injected via a needle, and the potential for the human body to automatically filter and remove a liquid droplet robot, make liquid droplet robots advantageous for medical applications; while the ability to remotely control the torques and forces on an untethered microrobot via modulating the magnetic field and gradient is also highly advantageous. The research described in this dissertation explores applications and methods for the electromagnetic control of ferrofluid droplet robots. First, basic electrical components built from fluidic channels containing ferrofluid are made remotely tunable via the placement of ferrofluid within the channel. Second, a ferrofluid droplet is shown to be fully controllable in position, stretch direction, and stretch length in two dimensions using proportional-integral-derivative (PID) controllers. Third, control of a ferrofluid’s position, stretch direction, and stretch length is extended to three dimensions, and control gains are optimized via a Bayesian optimization process to achieve higher accuracy. Finally, magnetic control of both single and multiple ferrofluid droplets in two dimensions is investigated via a visual model predictive control approach based on machine learning. These achievements take both liquid droplet robotics and magnetic micro-robotics fields several steps closer toward real-world medical applications such as embedded soft electronic health monitors, liquid-droplet-robot-based drug delivery, and automated magnetically actuated surgeries.