Here we describe some recent developments in analytical models that have been formulated in support of numerical and experimental studies of core gas dynamics appropriate of idealized rocket chambers. These analytical pursuits have invariably helped in providing additional physical insight while unraveling concrete parametric relations, explicit solutions, and group parameters of fundamental importance. In several practical applications, they have been invaluable in providing limiting process benchmarks needed to verify and, thereby, validate the reliability of numerical simulations. In many instances, they have enabled the specification of key similarity parameters that have been used to guide both experimental and numerical simulations. When equipped with perturbation tools, asymptotic methods have proven particularly useful in unveiling the essential features of acoustic instability mechanisms in rocket motors and other large combustors.