This paper reviews the current state-of-the-art in aircraft landing gear dynamics and presents recommendations for new areas of research in this field. The paper begins by reviewing some of the shortcomings the author has experienced in conducting shimmy investigations on various aircraft. Included in this review are the problems associated with obtaining both landing gear structural parameters and aircraft tire parameters. Some discussion is also made of the problems with current landing gear dynamics mathematical models. On the basis of all of these problems, recommendations are then made for future research. The main content of these recommendations are to develop three documents that will completely define a general landing gear dynamics mathematical/computer model that will be able to analyze the problems of gear walk, shimmy, dynamic response to rough runways, antiskid brake induced oscillations, tire-out-of-round, and wheel imbalance. The first document will completely define the mathematical model. The second document will update the TR-64 technical report by Smiley and Home on Mechanical Properties of Pneumatic Tires with Special Reference to Modern Aircraft Tires by examining both bias ply and radial tires. The third document will classify landing gear structures into various types in a manner similar to the way TR-64 defines tire types and then examines the structural parameters needed by the comprehensive mathematical model. The overall aim of the paper is to develop a unified, consistent approach to the design of landing gear systems.