In this paper, we construct a framework for modeling teams of agents who apply techniques or procedures (tools) to solve problems. In our framework, tools differ in their likelihood of solving the problem at hand; agents, who may be of different types, vary in their skill at using tools. We establish baseline hiring rules when a manager can dictate tool choice and then derive results for strategic tool choice by team members. We highlight three main findings: First, that cognitively diverse teams are more likely to solve problems in both settings. Second, that teams consisting of types that master diverse tools have an indirect strategic advantage because tool diversity facilitates coordination. Third, that strategic tool choice creates counterintuitive optimal hiring practices. For example, optimal teams may exclude the highest ability types and can include dominated types. In addition, optimal groups need not increase setwise. Our framework extends to cover teamwork on decomposable problems, to cases where individuals apply multiple tools, and to teams facing a flow or set of problems.