Cavity ringdown spectroscopy (CRDS) is a gas sensing technique in which an optical cavity is formed by two or more highly reflective mirrors. Herein we present an overview and historical perspective of CRDS implementations that seek to reduce or eliminate some of the disadvantages of conventional CRDS by modifications to the ringdown cavity (RDC). The hollow waveguide (HWG) CRDS concept that we introduce in this paper reduces some of the disadvantages of conventional CRDS by utilizing a hollow waveguide as the RDC. We develop the basic mathematical theory and model for the HWG-CRDS concept and provide an initial in-depth study of the Bragg waveguide for CRDS applications. We also discuss various aspects of design and performance characteristics of HWG-CRDS, including waveguide attenuation losses with and without gases in the waveguide core, transverse and longitudinal mode propagation behavior, and methods and analysis for the HWG-CRDS excitation.