The constant drive to replace rare-earth metal magnets has initiated great interest in an alternative. Manganese (Mn) has emerged to be a potential candidate as a key element in rare-earth-free magnets. Its five unpaired valence electrons give it a large magnetocrystalline energy and the ability to form several intermetallic compounds. These factors have led Mn-based magnets to be a potential replacement for rare-earth permanent magnets for several applications, such as efficient power electronics, energy generators, magnetic recording and tunneling applications, and spintronics. For past few decades, Mn-based magnets have been explored in many different forms, such as bulk magnets, thin films, and nanoparticles. Here, we review the recent progress in the synthesis and structure-magnetic property relationships of Mn-based rare-earth-free magnets (MnBi, MnAl and MnGa). Furthermore, we discuss their potential to replace rare-earth magnetic materials through the control of their structure and composition to achieve the theoretically predicted magnetic properties.