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In GMPLS-controlled optical networks, the utilization of source-based path computation has some limitations, especially in large networks with stringent constraints (e.g., optical impairments) or in multilayer and multidomain networks, which leads to suboptimal routing solutions. The path computation eElement (PCE) can mitigate some weaknesses of GMPLS-controlled optical networks. The main idea behind the PCE is to decouple the path computation function from the GMPLS controllers into a dedicated entity with an open and well-defined interface and protocol. A (stateless) PCE is capable of computing a network path or route based on a network graph (i.e., the traffic engineering database-TED) and applying computational constraints. First, we present an overview of the PCE architecture and its communication protocol (PCEP). Then, we present in detail the considered source-routing shortcomings in GMPLS-controlled networks, namely, impairment-aware path computation, multidomain path computation and multilayer path computation, as well as the different PCE-based solutions that have been proposed to overcome each one of these problems. However, PCE-based computation also presents some limitations that lead to an increase in the path computation blocking or to suboptimal path computations. The stateful PCE overcomes the limitations of the stateless PCE, such as the outdated TED, the lack of global LSP state (i.e., set of computed paths and reserved resources in use in the network), and the lack of control of path reservations. A passive stateful PCE allows optimal path computation and increased path computation success, considering both the network state (TED) and the Label Switched Paths (LSP) state (LSP Database-LSPDB). Additionally, an active stateful PCE can modify existing LSPs (i.e., connections), and optionally, setup and/or release existing LSPs. Finally, the formal decoupling of the path computation allows more flexibility in the deployment of PCEs in other control- paradigms outside their original scope (MPLS/GMPLS). In this sense, we provide an overview of three PCE deployment models in the software defined network (SDN) control architecture.