This chapter begins with an unspecified geometry, where the dielectric permittivity exhibits just one step discontinuity. It shows that a structure of this kind supports guided modes and unbounded modes and only a subset of the guided modes are transverse electric and Transverse Magnetic, while the others modes are hybrid. The chapter outlines why the exact analytical modes of step-index circular waveguides are too cumbersome, and how they can be replaced by approximate solutions, whose most interesting feature is that their transverse fields are linearly polarized. It focuses on dispersion in dielectric rods, a very important issue in characterizing optical fibers. The chapter describes graded-index waveguides, show how they can be studied with approximate analytical techniques, and discusses their performance limitations. It also focuses on losses in dielectric waveguides. The chapter summarizes at any finite value of the frequency a dielectric waveguide supports: a finite number of guided modes, a continuum of radiation modes and a continuum of evanescent modes.