\he rapid growth in wireless devices and the spread of wireless communication systems has increased the demand for energy sources. Therefore reliable energy sources should be provided to guarantee effective performance of wireless networks. Although energy storages and batteries provide a convenient solution, they can not be used as the sole power source in the long run. Moreover in some cases battery replacements can be challenging and expensive or in some areas impossible. In recent years, energy harvesting (EH) technologies has emerged as a promising method to power the nodes of a wireless communication network. Energy harvesting communicatio are able to harvest ambient energy from their surrounding environment, and are therefore less dependent to non-renewable energy sources and can enjoy a prolonged lifetime. The rechargeable battery in an energy harvesting transmitter or receiver can serve as the primary or a backup power source. The idea of using renewable ambient energy sources rises the possibility of having green communication networks. Using energy harvesting devices in communication systems changes the nature of the challenges faced when designing optimal performance schemes for such networks. The main challenge in the design of energy harvesting communications systems is that the available energy at any time instance is essentially a random variable. In other words, the ambient energy becomes available at the nodes in random quantities and at random times throughout the communication horizon. Hence, optimal transmission policies, that account for the time-varying available energy, must be designed so that the network can exploit this random ambient energy arrivals in the most efficient way. This thesis investigated the problem of designing optimal transmission policies for energy harvesting cooperative communication systems. We considered a decode-and-forward relay network with an energy harvesting source and an energy harvesting relay. We consider the direct link between source and the destination, as well. The throughput maximization problem over a finite horizon of N transmission blocks is investigated. In the first part of this thesis, we examined the problem of total throughput maximization for the energy harvesting network in the offline setting. In this case, we assumed that the information of the energy harvesting and channel fading profiles are available prior to the beginning of the transmission. The results obtained in this part serve as the performance upper-bound for the energy harvesting communication system under consideration. In the second part of this thesis, we considered the more practical online setting, where the energy arrival information and the channel states information is known causally. For this case dynamic programming can be used which is the conventional approach for solving stochastic control problems. Dynamic programming in general has a high computational complexity. we used a method based on Markov decision processes to obtain power-optimal transmission policies. I MDP formulation, we have considered discrete state space for the system. Furthermore, the transmission power was chosen from a set of discrete and finite power levels. This approach makes the problem tractable to be solved. Implementing the MDP formulation needs certain computational and memory requirements, so there has bee some suboptimal solutions. The optimal and also suboptimal methods are simulated to obtain the power levels. The performance of the introduced schemes are evaluated using computer simulations and are compared to existing methods which address the same problem. Keywords: 1- Energy Harvesting, 2- Cooperative Communication, 3- Relay Channel 4- Convex Optimization, 5- Markov Decision Process