This thesis presents two state-of-the-art systems approaches to statistical modelling of fuel efficiency in ship propulsion: a regression model and a dynamical model. Three statistical regression model approaches are investigated and compared: Artificial Neural Networks (ANN), Gaussian processes (GP), and Gaussian Mixture Models (GMM). A dynamical modelling approach is introduced. This modelling approach has not been used before in the context of ship propulsion modelling, and solves problems encountered with the regression model in an onboard trim optimization application. The dynamical model is introduces through a study of the wellknown sunspot time series, and then on ship data. The dynamical modelling approach is investigated using both the Artificial Neural Network and the Gaussian mixture model. The thesis also presentes a novel and publicly available data set of high quality sensory data on which all the models are based and tested. No other similar publicly available data set exists. The data presented is a publicly available full-scale data set, with a whole range of features sampled over a period of 2 months. The data is online with an accompanying homepage, where all the results are also presented.