Road traffic is important to everybody in the world. People travel and commute everyday. For those who travel by cars (or other types of road vehicles), traffic congestion is a daily experience. One essential goal of traffic researchers is to reduce traffic congestion and to improve the whole traffic system operation and the environment. To achieve this goal, we have to first understand prevailing traffic situations, then perform pro-active traffic control and management. The estimation of traffic states in the past, in the present and in the future plays an important role in traffic management and control systems. This thesis focuses on the development of traffic state estimation approaches, which provide such traffic state information. In road networks, traffic states refer to typical quantities, such as travel times, traffic speeds, traffic flow and density. These quantities reflect the traffic conditions. Based on these data, we are able to find out when a traffic jam starts, or where a traffic accident occurs. However, it is not feasible to get the full picture of traffic states from the current monitoring systems. Due to cost and technical constraints, we can only obtain spatially and temporally discretised traffic data. These traffic data are collected mainly from point-based sensors, such as inductive loops, radars, and cameras. Alternatively, traffic information might be observed by probe vehicles with a selected penetration rate. In all cases, the detected data usually contain errors and noise, which might hinder further analyses. Based on these constraints, this thesis aims to develop a traffic state estimation procedure to solve the foregoing problems and to provide accurate and complete traffic state information. In this procedure, both traffic flow models and the available observation data are used to estimate the most probable traffic states within a data-assimilation framework. Our approach is formulated using a moving observer perspective, resulting in a Lagrangian formulation of traffic state estimation. In the Lagrangian coordinate system, coordinates move with the vehicles. The Lagrangian formulated first-order traffic flow model is applied to describe the evolution of traffic state variables. The proposed Lagrangian formulation of traffic state estimation offers both theoretical and computational advantages over the conventional Eulerian formation. Moreover, this approach can capture the dynamics of multiple vehicle classes by implementing a multi-class traffic flow model. In this thesis, data pre-processing methods are also developed to improve the quality of the observation inputs. Both Eulerian and Lagrangian sensing data are incorporated into the state estimation. The online technique, known as the Extended Kalman Filter (EKF), is applied for data assimilation: this combines traffic model prediction with observation input correction. Importantly, the Lagrangian concept is not restricted to the EKF method with the first-order traffic flow model, but can also be applied to other data-assimilation techniques in combination with more involved macroscopic traffic flow models. A series of experimental studies based on both synthetic and real-world data have been performed to test the proposed methodology. These studies have validated both the mixed-class and the multi-class traffic state estimation methods. The results have demonstrated that the Lagrangian traffic state estimation outperforms the Eulerian approaches in the EKF-based framework, and the multi-class approach further improves the performance of state estimation compared with the mixed-class case. In summary, Lagrangian multi-class state estimation can provide accurate class-specific traffic information for class-specific control applications and traffic management.