Nano-photonic waveguides are categorized into three types: silicon (Si) photonics, photonic crystals, and surface plasmons. Si photonics is based on integrated high refractive-index contrast Si-on-insulator (SOI) waveguides with nano-scale widths and thicknesses called nano-wires (NWs). This chapter surveys fundamentals of Si photonics based on the conventional dielectric optical waveguides, that is, mode theories, geometries, materials, and device configurations: First, guided mode theories and dispersion properties are described based on ray-optics and electromagnetic-wave approaches. Second, two- to three-dimensional waveguide structures and materials are surveyed. Finally, configurations and functions of typical passive waveguides as core elements of Si photonic platform are surveyed. They include interferometric waveguides, directional couplers, optical resonators, arrayed waveguide gratings, polarization beam splitters/rotators, and fiber-to-chip light couplers. Applications of Si photonic waveguides such as hybrid lasers, detectors, modulators/switches are described in Chap.  4 (optical transceiver and switch) and Chap.  5 (LiDAR and optical neural network).