This volume contains the proceedings of the AMS Special Session on New Developments in the Analysis of Nonlocal Operators, held from October 28-30, 2016, at the University of St. Thomas, Minneapolis, Minnesota. Problems represented in this volume include uniqueness for weak solutions to abstract parabolic equations with fractional time derivatives and the behavior of the one-phase Bernoulli-type free boundary near a fixed boundary and its relation to a Signorini-type problem.