To introduce the concepts of “surface” and “leaky” wave, the two types of electromagnetic boundary wares that will chiefly concern us, we begin with the concrete example of an e-lectric line source exciting a grounded dielectric slab (Sec.l). By generalizing various features of this example, we can display the entire spectrum of boundary waves (Sec.2). This is followed by a discussion of surface waveguides (Sec.3). We conclude with a brief description of radiation from surface and leaky waves, with application to traveling-wave antennas (Sec.4).