We consider partially observed linear quadratic Gaussian control over communication networks in which the forward channel transporting measurements is modeled by a zero-delay packet-deletion channel and the feedback channel transporting control inputs is assumed ideal. We characterize the optimal control and the optimal sampling policies that achieve the minimum data rate required for a guaranteed level of control performance. We prove that for event driven sampling the adopted filter is optimal and the separation principle between control and estimation holds. We show that the optimal control policy is a certainty equivalent policy and the optimal sampling policy is a threshold policy expressed in terms of the value of information. We prove that the value of information is a quadratic function of the innovation. We describe generalizations to other information constraints, multi-agent systems and dynamic games.