The paper reviews numerical and experimental investigations concerned with the physics of rising bubbles in conducting liquid metals under the action of a magnetic field. Different situations, characterized by different void fractions ranging from single bubbles to bubble swarms, are considered. The impact of the geometrical arrangement is addressed covering large containers with bubbles far from the walls and narrow containers with bubbles interacting with the walls. It is demonstrated that magnetic fields offer a convenient means to influence bubble dynamics, which makes them interesting for technological applications.