The U.S. Army has long confronted problems at the frontiers of computational technology. During World War II such applications motivated the development of ENIAC. By the 1960s, solid modeling and what we now know as computational geometry had become critical tools in the development and use of munitions and other military systems.In this talk I present several current applications of geometric computing in fields such as penetration mechanics, electrooptics, and vulnerability analysis. My goal is similar to those of the CG Impact Task Force in compiling its Application Challenges: to offer some problems the investigation of which might stimulate computational geometry research and the solution of which would ultimately be highly valuable in saving soldiers' lives.