Ocean waves represent an untapped source of renewable energy which can significantly contribute to the energy transition towards a sustainable energy mix. Despite the significant potential of this energy source and the multiple solutions suggested for the extraction of energy from ocean waves, some of which have demonstrated to be technically viable, no commercial wave energy farm has yet been connected to the electricity grid. This means that none of the technologies suggested in the literature has achieved economic viability. In order to make wave energy converters economically viable, it is essential to accurately understand and evaluate the holistic behaviour and performance of wave energy converters, including all the different conversion stages from ocean waves to the electricity grid. This can be achieved through wave tank or open ocean testing campaigns, which are extremely expensive and, thus, can critically determine the financial sustainability of the developing organisation, due to the risk of such large investments. Therefore, precise mathematical models that consider all the important dynamics, losses and constraints of the different conversion stages (including wave-structure hydrodynamic interaction and power take-off system), known as wave-to-wire models, are crucial in the development of successful wave energy converters. Hence, a comprehensive literature review of the different mathematical approaches suggested for modelling the different conversion stages and existing wave-to-wire models is presented, defining the foundations of parsimonious wave-to-wire models and their potential applications. As opposed to other offshore applications, wave energy converters need to exaggerate their motion to maximise energy absorption from ocean waves, which breaks the assumption of small body motion upon which linear models are based. An extensive investigation on the suitability of linear models and the relevance of different nonlinear effects is carried out, where control conditions are shown to play an important role. Hence, a computationally efficient mathematical model that incorporates nonlinear Froude-Krylov forces and viscous effects is presented. In the case of the power take-off system, mathematical models for different hydraulic transmission system configurations and electric generator topologies are presented, where the main losses are included using specific loss models with parameters identified via manufacturers’ data. In order to gain confidence in the mathematical models, the models corresponding to the different conversion stages are validated separately against either high-fidelity well-established software or experimental results, showing very good agreement. The main objective of this thesis is the development of a comprehensive wave-to-wire model. This comprehensive wave-to-wire model is created by adequately combining the subsystems corresponding to the different components or conversion stages. However, time-step requirements vary significantly depending on the dynamics included in each subsystem. Hence, if the time-step required for capturing the fastest dynamics is used in all the subsystems, unnecessary computation is performed in the subsystems with slower dynamics. Therefore, a multi-rate time-integration scheme is implemented, meaning that each subsystem uses the sample period required to adequately capture the dynamics of the components included in that conversion stage, which significantly reduces the overall computational requirements. In addition, the relevance of using a high-fidelity comprehensive wave-to-wire model in accurately designing wave energy converters and assessing their capabilities is demonstrated. For example, energy maximising controllers based on excessively simplified mathematical models result in dramatic consequences, such as negative average generated power or situations where the device remains stuck at one of the end-stops of the power take-off system. Despite the reasonably high-fidelity of the results provided by this comprehensive wave-towire model, some applications require the highest possible fidelity level and have no limitation with respect to computational cost. Hence, the simulation platform HiFiWEC, which couples a numerical wave tank based on computational fluid dynamics to the high-fidelity power take-off model, is created. In contrast, low computational cost is the main requirement for other applications and, thus, a systematic complexity reduction approach is suggested in this thesis, significantly reducing the computational cost of the HiFiWEC platform, while retaining the adequate fidelity level for each application. Due to the relevance of the nonlinearity degree when evaluating the complexity of a mathematical model, two nonlinearity measures to quantify this nonlinearity degree are defined. Hence, wave-to-wire models specifically created for each application are generated via the systematic complexity reduction approach, which provide the adequate trade-off between computational cost and fidelity level required for each application.