The ideal transformer is a simple device whose analysis is covered in most electrical engineering textbooks, encompassing power systems, circuit analysis and basic electromagnetics. Ordinary analysis of ideal transformer functioning poses several delicate physical questions whose answer is given in this paper, enabling an understanding of the whole picture. On one hand, it is shown that if the magnetic stray flux is absent (as usually is assumed), then power flow between primary and secondary windings cannot occur. On the other hand, a physically correct perspective to deal with ideal transformers is developed by resorting to frequency-domain transmission line theory. This approach, based on Maxwell's equations and Poynting's vector, applies indistinctly to low and high frequency regimes. For analysis purposes the ideal transformer is modeled by means of an ideal magnetic transmission line. Transverse electric and magnetic fields (TEM) are obtained considering the particular example of a coaxial geometry. Ordinary results concerning the ideal transformer, i.e., voltage, current, and impedance ratios, are thoroughly discussed.