This thesis examines the use of modelling approaches in Wireless Sensor Networks (WSNs) at node and sink to: reduce the amount of data that needs to be transmitted by each node and estimate sensor readings for locations where no data is available. First, to contextualise the contributions in this thesis, a framework for WSN monitoring applications (FieldMAP) is proposed. FieldMAP provides a structure for developing monitoring applications that advocates the use of modelling to improve the informational output of WSNs and goes beyond the sense- and-send approach commonly found in current, elded WSN applications. Rather than report raw sensor readings, FieldMAP advocates the use of a state vector to encapsulate the state of the phenomena sensed by the node. Second, the Spanish Inquisition Protocol (SIP) is presented. SIP reduces the amount of data that a sensor node must transmit by combining model-based ltering with Dual-Prediction approaches. SIP makes use of the state vector component of FieldMAP to form a simple predictive model that allows the sink to estimate sensor readings without requiring regular updates from the node. Transmissions are only made when the node detects that the predictive model no longer matches the evolving data stream. SIP is shown to produce up to a 99% reduction in the number of samples that require transmission on certain data sets using a simple linear approach and consistently outperforms comparable algorithms when used to compress the same data streams. Furthermore, the relationship between the user-specied error threshold and number of transmissions required to reconstruct a data set is explored, and a method to estimate the number of transmissions required to reconstruct the data stream at a given error threshold is proposed. When multiple parameters are sensed by a node, SIP allows them to be combined into a single state vector. This is demonstrated to further reduce the number of model updates required compared to processing each sensor stream individually. iii Third, a sink-based, on-line mechanism to impute missing sensor values and predict future readings from sensor nodes is developed and evaluated in the context of an on-line monitoring system for a Water Distribution System (WDS). The mechanism is based on a machine learning approach called Gaussian Process Regression (GPR), and is implemented such that it can exploit correlations between nodes in the network to improve predictions. An on-line windowing algorithm deals with data arriving out of order and provides a feedback mechanism to predict values when data is not received in a timely manner. A novel approach to create virtual sensors that allows a data stream to be predicted where no physical sensor is permanently deployed is developed from the on-line GPR mechanism. The use of correlation in prediction is shown to improve the accuracy of predicted data from 1.55 Pounds per Square Inch (PSI) Root Mean Squared Error (RMSE) to 0.01 PSI RMSE. In-situ evaluation of the Virtual Sensors approach over 36 days showed that an accuracy of 0:75 PSI was maintained. The protocols developed in this thesis present an opportunity to improve the output of environmental monitoring applications. By improving energy consumption, long-lived networks that collect detailed data are made possible. Furthermore, the utility of the data collected by these networks is increased by using it to improve coverage over areas where measurements are not taken or available.