Magneto-Electroencephalogram(M/EEG)-based neuroimaging is a widely used technique that allows to non invasively explore brain activity. One of the most prominent advantages of using M/EEG measures to analyze brain activity is its outstanding temporal resolution. However, spatial measurement points (electrodes) are relatively low -a couple hundreds in the best case-, while the discretized brain activity generators -termed current dipoles or sources- are several thousands. This leads to a heavily ill-posed mathematical problem commonly known as the M/EEG inverse problem. To solve such problems, additional information must be a-priori assumed in order to obtain an unique and optimal solution. In the present work, several approaches to improve the accuracy and interpretability of the inverse problem solution are proposed, using physiologically motivated assumptions. Firstly, a method that infers neural states from the M/EEG recordings to dynamically constraint the M/EEG inverse problem is proposed, relaxing the brain activity stationarity assumption that is usually made in state-of-art algorithms. This is done by assuming a physiologically motivated time-varying a-priori covariance matrix. Secondly, a realistic time varying autoregressive model is proposed, aiming to explicitly constraining temporal evolution of brain activity. Finally, a novel source connectivity analysis method is proposed by taking advantage of the temporal dynamics provided by the M/EEG recordings. The proposed methods are compared with classic and state-of-art techniques in a simulated environment, and afterwards, are validated using real world data. In general, the contributed approaches are efficient and competitive compared to state-of-art brain mapping and source connectivity methods