Pulsars (otherwise known as neutron stars) were predicted in the 1930's and discovered in the 1960's. The discovery came as a surprise, because up until that moment, no one expected pulsars to generate any kind of detectable emission (if they existed at all). Thankfully, they were discovered, and this discovery has opened up whole new areas of research, pushing the frontiers of dense matter physics, strong-field gravitation, gravitational wave detection, and relativistic plasma.
Upon their discovery, one of the immediate questions to be answered was: "How are they emitting radiation at all?" That is to say, given that the radiation we see is made up of photons, how are those photons generated? For example, in the case of ordinary stars, photons are produced as a byproduct of nuclear fusion reactions catalysed by tremendous heat and pressure. By the time they escape the star's photosphere, they have achieved thermal equilibrium with the star's outer layers of plasma and appear to us as an approximate blackbody spectrum. All of this was worked out in the first half of the 20th century; many details of the explanation depended crucially on the recently discovered principles of Special Relativity and Quantum Mechanics, so it could not have been worked out any sooner. There are of course several stars that "behave unusually" in the sense that their observed properties deviate from the predictions of stellar theory, but it is widely believed that these can be accounted for by enlarging the theory to take into account a wider set of environmental parameters (e.g. the presence of heavier elements, or the star's interaction with its environment). In other words, it is believed that the variety of stellar properties can be explained by the complexity of individual systems; however, our understanding of the physics that govern the emission processes—i.e. the emission mechanism itself—is believed to be basically correct.
Over the decades, several distinct kinds of emission mechanisms have been employed to explain different kinds of astrophysical phenomena. These include (but are not limited to) thermal, (atomic) spectral line, maser, synchrotron, and bremsstrahlung emission. Each emission mechanism describes a unique set of interactions between particles on atomic and subatomic scales. They should be considered distinct processes, and not different manifestations of the same process. One of the main goals of astrophysics is to identify
For pulsars, it didn't happen that way at all. The positive identification of pulsars as rapidly rotating neutron stars was based on