Numerical models often fail to accurately simulate and forecast a hydrological state in operation due to its inherent uncertainties. Data Assimilation (DA) is a promising technology that uses real-time observations to modify a model's parameters and internal variables to make it more representative of the actual state of the system it describes. In this thesis, hydrological DA is first reviewed from the perspective of its objective, scope, applications and the challenges it faces. Special attention is then given to nonlinear Kalman filters such as the Extended Kalman Filter (EKF). Based on a review of the existing studies, it is found that the potential of EKF has not been fully exploited. The Soil and Water Assessment Tool (SWAT) is a semi-distributed rainfall-runoff model that is widely used in agricultural water management and flood forecasting. However, studies of hydrological DA that are based on distributed models are relatively rare because hydrological DA is still in its infancy, with many issues to be resolved, and linear statistical models and lumped rainfall-runoff models are often used for the sake of simplicity. This study aims to fill this gap by assimilating streamflow and surface soil moisture observations into the SWAT model to improve its state simulation and forecasting capability. Unless specifically defined, all 'forecasts' in Italic font are based on the assumption of a perfect knowledge of the meteorological forecast. EKF is chosen as the DA method for its solid theoretical basis and parsimonious implementation procedures. Given the large number of parameters and storage variables in SWAT, only the watershed scale variables are included in the state vector, and the Hydrological Response Unit (HRU) scale variables are updated with the a posteriori/a priori ratio of their watershed scale counterparts. The Jacobian matrix is calculated numerically by perturbing the state variables. Two case studies are carried out with real observation data in order to verify the effectiveness of EKF assimilation. The upstream section of the Senegal River (above Bakel station) in western Africa is chosen for the streamflow assimilation, and the USDA ARS Little Washita experimental watershed is chosen to examine surface soil moisture assimilation. In the case of streamflow assimilation, a spinoff study is conducted to compare EKF state-parameter assimilation with a linear autoregressive (AR) output assimilation to improve SWAT's flood forecasting capability. The influence of precipitation forecast uncertainty on the effectiveness of EKF assimilation is discussed in the context of surface soil moisture assimilation. In streamflow assimilation, EKF was found to be effective mostly in the wet season due to the weak connection between runoff, soil moisture and the curve number (CN2) in dry seasons. Both soil moisture and CN2 were significantly updated in the wet season despite having opposite update patterns. The flood forecast is moderately improved for up to seven days, especially in the flood period by applying the EKF subsequent open loop (EKFsOL) scheme. The forecast is further improved with a newly designed quasi-error update scheme. Comparison between EKF and AR output assimilation in flood forecasting reveals that while both methods can improve forecast accuracy, their performance is influenced by the hydrological regime of the particular year. EKF outperformed the AR model in dry years, while AR outperformed the EKF in wet years. Compared to AR, EKF is more robust and less sensitive to the length of the forecast lead time. A combined EKF-AR method provides satisfying results in both dry and wet years. The assimilation of surface soil moisture is proved effective in improving the full profile soil moisture and streamflow estimate. The setting of state and observation vector has a great impact on the assimilation results. The state vector with streamflow and all-layer soil moisture outperforms other, more complicated state vectors, including those augmented with intermediate variables and model parameters. The joint assimilation of surface soil moisture and streamflow observation provides a much better estimate of soil moisture compared to assimilating the streamflow only. The updated SWAT model is sufficiently robust to issue improved forecasts of soil moisture and streamflow after the assimilation is 'unplugged'. The error quantification is found to be critical to the performance of EKF assimilation. Nevertheless, the application of an adaptive EKF shows no advantages over using the trial and error method in determining time-invariant model errors. The robustness of EKF assimilation is further verified by explicitly perturbing the precipitation 'forecast' in the EKF subsequent forecasts. The open loop model without previous EKF update is more vulnerable to erroneous precipitation estimates. Compared to streamflow forecasting, soil moisture forecasting is found to be more resilient to erroneous precipitation input.