This paper studies the question: Why are there Firms? Motivated by observations of a variety of economies, several distinct concepts of what it means to be a firm are identified and then analyzed with mechanism design models. In the first class of models, a group of individuals is a firm if they collude and share information. This model is analyzed and compared with the non-firm alternative. Conditions are provided in which firms are preferred to no firms and vice versa. Next, we show how an economy with multiple distinct groups of colluding individuals can be decentralized.In the next class of models, collusion is prohibited, but the information structure of the economy depends on whether individuals work together. Activities performed jointly by the individuals are considered to be done with a firm. In the model the degree of economic activity organized by firms is endogenous. Numerical examples are provided in which none, some, and all work is done within a firm. The last class of models studies the long-term nature of firms versus the short-term nature of non- firm arrangements, like spot markets. Multi-stage models are developed in which individuals may be switched between projects. People who work the same project over time are considered to work for a firm. Conditions for the optimality of long-term and short-term arrangements are provided.