Today's power generation and distribution networks are quickly moving toward automated control and integration of renewable resources - a complex, integrated system termed the Smart Grid. A key component in planning and managing of Smart Grids is State Estimation (SE). The state-of-the art SE technologies today operate on the basis of slow varying dynamics of the current network and make simplifying linearity assumptions. However, the integration of smart readers and green resources will result in significant non-linearity and unpredictability in the network. Therefore in future Smart Grids, there is need for ever more accurate and real-time algorithms. In this work, we propose and examine new SE methods that aim to achieve these measures by approximating the true distribution of the state variables, rather than a linearized version as done for instance in Kalman filtering. Through simulations we show that in the presence of non-linearities and non-Gaussian noise, our general SE framework improves accuracy where linear and Kalman-like filters exhibit impaired performance.