I will describe explanations of 1) Michelson-Morley type experiments, 2) Muon decay puzzle, and 3) Doppler’s effect in light. The explanation of Michelson-Morley type experiments is based on the emission-wave mechanism. The resolution of the muon decay puzzle is then based on Pauli’s exclusion principle as applied to a system of interacting muon and electrons surrounding it during its passage in the Earth’s atmosphere. The explanation of the Doppler shift in frequency is then based on the analysis of proper locations on the light fronts. Notably, these explanations do not involve either the time-dilation or the length contraction as in the Special Theory of Relativity. That is to say, these explanations do not use the Lorentz transformations. Nevertheless, they are based on the principle that the speed of light is the same for all observers, whether accelerated or not. These results then render the concepts of special relativity, like time-dilation and length-contraction, to be inessential for physics, in general. But, these results are consistent with the framework of the Universal Theory of Relativity that allows for universal time running at the same rate for all observers and are definite pointers to subtlety in the applications of the concepts of relativity, therefore.