Problems of singular stochastic control (SSC) and optimal stopping (OS) arise frequently in Economics and Finance. Examples of applications are capacity choice, optimal management of storage systems, entry/exit problems, and fair pricing of American options. In this project we study games of SSC and games of OS. In particular, we aim at investigating if there exists a connection between certain games of SSC and suitable nonzero-sum games of OS that is consistent with the link OS-SSC observed in single-agent optimization problems. Moreover, we will consider zero-sum games of OS with incomplete information, SSC problems with multi-dimensional controls and games involving impulse controls. For the latter two topics, possible relations with questions of OS will also be explored.