Topological band theory has revolutionized the understanding of electronic band structure in condensed matter and led to the discovery of novel material classes, such as topological semimetals, topological and magnetic topological insulators. The emerging field of altermagnetism combines the merits of both ferromagnets and antiferromagnets, which were until recently regarded as incompatible. Consequently, they exhibit phenomena unmatched by either of the two traditional magnetic phases. Combining topological protection with altermagnetically lifted spin-degeneracy promises unprecedented robustness and potential mediation of altermagnetic spin-transport properties of bulk to the surface. Understanding the fundamental mechanism of their formation promises far-reaching implications in the fields of spintronics, quantum and neuromorphic computing and superconductivity.