A digital microfluidic platform manipulates droplets on an open surface. Magnetic digital microfluidics utilizes magnetic forces for actuation and offers unique advantages compared to other digital microfluidic platforms. First, the magnetic particles used in magnetic digital microfluidics have multiple functions. In addition to serving as actuators, they also provide a functional solid substrate for molecule binding, which enables a wide range of applications in molecular diagnostics and immunodiagnostics. Second, magnetic digital microfluidics can be manually operated in a "power-free" manner, which allows for operation in low-resource environments for point-of-care diagnostics where even batteries are considered a luxury item. This review covers research areas related to magnetic digital microfluidics. This paper first summarizes the current development of magnetic digital microfluidics. Various methods of droplet manipulation using magnetic forces are discussed, ranging from conventional magnetic particle-based actuation to the recent development of ferrofluids and magnetic liquid marbles. This paper also discusses several new approaches that use magnetically controlled flexible substrates for droplet manipulation. In addition, we emphasize applications of magnetic digital microfluidics in biosensing and medical diagnostics, and identify the current limitations of magnetic digital microfluidics. We provide a perspective on possible solutions to close these gaps. Finally, the paper discusses the future improvement of magnetic digital microfluidics to explore potential new research directions.