Wireless Sensor Networks (WSNs) have emerged as a new research area in communication systems in recent years. Theoretically, sensor networks can be modeled by either Chief Executive Officer (CEO) problem or Multi-terminal communication problem. A Wireless Sensor Network consists of a set of battery-powered nodes which are limited in energy; and network's lifetime depends on the energy consumption of the nodes. Therefore, one of the main issues in designing WSNs is reducing the energy consumption. In sensor networks we deal with a set of correlated observations. We can exploit this correlation and compress the data which is going to be transmitted from different nodes. Moreover, as all nodes are equipped with antennas, we can take advantage of having several antennas and apply advanced energy-efficient communication methods such as Multiple-Input Multiple-Output (MIMO) technique.  The contributions of this thesis are presented in two parts: In the first part we consider the Chief Executive Officer (CEO) problem for binary sources. We model the source by an i.i.d. unbiased sequence which is connected to each sensor via a Binary Symmetric Channel (BSC). We analyze the behavior of the system and show that sensors can compress their observations according to Slepian-Wolf rate bound. We consider the conditional entropy of the source given a set of observations as a function of number of sensors as well as cross-over probability of the BSC. We derive a closed form for this function and prove that it converges to zero as the number of sensors tends to infinity. Substituting this function in Fano's inequality, we determine the minimum number of sensors required to achieve a desired probability of error. We also derive the estimation rule for a Maximum Likelihood estimator.  In the second part we consider cooperative communication where sensors are able to communicate in order to jointly compress their correlated information and apply MIMO transmission techniques. We assume two scenarios. In the first scenario we consider the Gaussian CEO problem where sensors observe a common Gaussian source and report noisy versions of this source to the CEO. We propose an energy-efficient cooperative algorithm for data estimation exploiting virtual MIMO technique. In the second scenario we extend the problem to Multi-terminal communication where all nodes wish to transfer their individual correlated information to the Fusion Center which is interested in all observations. We propose two different cooperative data compression algorithms. In the first algorithm we transform the correlated data into parallel independent Gaussian sources. We derive mathematical closed form equations for the transform matrices and optimum rate allocation. In the second algorithm we apply Vector Quantization. We simulate the proposed algorithms and compare their performance