Advances in fabrication, modern sensor and communication technologies, and computer architecture have enabled a variety of new networked sensing and control applications. However, many difficulties are inherent with these systems, for example, the constrained communication and computation capabilities, and limited energy resources, which are frequently seen in a wireless sensor network. As a consequence, the networks typically induce many new issues such as limited bandwidth, packet loss, and delay. Estimation and control over such networks thus require new design paradigms beyond traditional sampled-data control, as the aforementioned constraints undoubtedly affect system performance or even stability. In this thesis work, I consider the problem of state estimation over networks. As communication, computation, and energy are scarce resources in such networks, I focus on optimizing the use of them. When the state estimation is carried out over a sensor network, I consider the problem of minimizing the sensor energy usage and maximizing the network lifetime. When the state estimation is carried out over a packet-delaying network, I consider the problem of minimizing the buffer length at the remote state estimator. In each scenario, a certain desired level of estimation quality is guaranteed.