Micro-magnetofluidics refers to the science and technology that combines magnetism with microfluidics to gain new functiolities. Magnetism has been used for actuation, manipulation and detection in microfluidics. In turn, microfluidic phenome can be used for making tuble magnetic devices. This paper presents a systematic review on the interactions between magnetism and fluid flow on the microscale. The review rather focuses on physical and engineering aspects of micro-magnetofluidics, than on the biological applications which have been addressed in a number of previous excellent reviews. The field of micro-magnetofluidics can be categorized according to the type of the working fluids and the associated microscale phenome of established research fields such as magnetohydrodymics, ferrohydrodymics, magnetorheology and magnetophoresis. Furthermore, similar to microfluidics the field can also be categorized as continuous and digital micro-magnetofluidics. Starting with the alysis of possible magnetic forces in microscale and the impact of miniaturization on these forces, the paper revisits the use of magnetism for controlling fluidic functions such as pumping, mixing, magnetowetting as well as magnetic manipulation of particles. Based on the observations made with the state of the art of the field micro-magnetofluidics, the paper presents some perspectives on the possible future development of this field. While the use of magnetism in microfluidics is relatively established, possible new phenome and applications can be explored by utilizing flow of magnetic and electrically conducting fluids.