Quantum entanglement is a physical resource that is essential for many quantum information processing tasks, such as quantum communication and quantum computing. Although entanglement is essential for practical implementations in those fields, it is hard to create and transmit entanglement reliably. External factors introduce noise which may destroy or weaken the entanglement. Consequently, there is a need for methods to improve entanglement. Entanglement distillation attempts to solve this problem. Entanglement distillation is a process where probabilistically from a fixed number of copies of noisy entangled states, a smaller number of more strongly entangled states is created. This is done using only local operations and classical communication. Various protocols are known to perform distillation. However, for many it is unknown whether better results are possible. The goal of this thesis is to show whether known protocols are optimal. The greatest amount of entanglement achievable by entanglement distillation can be expressed as a non-convex optimization problem over separable quantum states. This problem is further relaxed to a semide finite program which will yield upper bounds on performance of the distillation for specific input states. The program is applied to various states that occur in experimental setups. Two known protocols are shown to perform on the upper bound, thus, being optimal. Using a heuristic algorithm, we look for new protocols. Here the optimization is done iteratively over one quantum state at a time. However, this method did not result in any useful protocols.