Special relativity (alternative formulations)
Hendrik Lorentz and Henri Poincaré developed their version of special relativity in a series of papers from about 1900 to 1905. They used Maxwell's equations and the principle of relativity to deduce a theory that is mathematically equivalent to the theory later developed by Einstein.
Einstein's thought experiments
In a 1920 review on the "Fundamental Ideas and Methods of the Theory of Relativity" (unpublished), Einstein related how disturbing he found this asymmetry: 
Einstein needed to extend the relativity of motion that he perceived between magnet and conductor in the above thought experiment to a full theory. For years, however, he did not know how this might be done. The exact path that Einstein took to resolve this issue is unknown. We do know, however, that Einstein spent several years pursuing an emission theory of light, encountering difficulties that eventually led him to give up the attempt. 
That decision ultimately led to his development of special relativity as a theory founded on two postulates of which he could be sure. Expressed in contemporary physics vocabulary, his postulates were as follows: