**Abstract:** Formation control deals with the design of control laws for multi-agent systems in which agents are required to stabilize at prescribed distances from each other. The most interesting cases, both in theory and practice, arise when agents only have access to partial information about the state and the objective of the system — we refer to this scenario as formation control with localized information. After formally introducing formation control, we will establish several fundamental limitations stemming from the information localization: first, we will show that for many formations, local stabilization around prescribed distances requires agents to know the objectives of agents whose states they cannot observe. Second, we will show that information localization can force the appearance of undesired, yet locally stable equilibria. Finally, if time permits, we will show that an often-used gradient-type control law is not robust to mismatch in the objectives.