A grounded dielectric slab covered with a metal strip grating in the form of an infinite linear array of microstrip lines constitutes a canonical structure for the realization of a variety of microwave components and antennas, including artificially hard and soft surfaces. In this contribution we review some recent theoretical and numerical results concerning surface and leaky waves supported by this structure. Spectral properties of modes propagating at arbitrary angles in the plane of the strip grating are examined, in order to provide criteria for the correct study of modal evolution as a function of frequency or propagation angle. Numerical full-wave results are provided that illustrate some interesting and novel properties related to such modal evolutions