Technical Abstract: This paper, written by the winners of the Don and Betty Kirkham Award in Soil Physics, is dedicated to the legacy of Don Kirkham. It describes eight longstanding or emerging research areas in soil physics that contain key unsolved problems. All are field-oriented with applications to a number of important issues in agriculture and the environment. The first class of problems concerns characterization of field-scale soil water properties, within which we describe progress on scaling, effective hydraulic properties, and the relationship between soil structure and function. We then move to the description of unstable flow and characterizing water repellency, and finish with discussions on the effect of plants on transport processes, characterizing soil microbial diversity, and the importance of soil ecological infrastructure in providing ecosystem services. Progress made within each area is elucidated, and roadblocks to the solution of the remaining problems are identified.