This PhD thesis contributes towards extending connectivity analyses and neurocomputational modelling of brain activities, and their applications. It starts with a brief review of different classes of neural models with different levels of realism. A main focus is the neural mass models (NMMs) that account for the collective behaviour of neuronal populations striking a balance between mathematical simplicity and biological plausibility, and hence suitable for large-scale neural circuit modelling. This is followed by a review on two popular large-scale neural connectivity frameworks, dynamic causal modelling (DCM) and Granger causal modelling (GCM), with a focus on human neuroimaging data. The thesis has led to four original research contributions. In the first contribution, a fully self-feedback model (FSM) is introduced as an extension to existing NMMs. FSM contains extra sel£feedback loops in both excitatory and inhibitory subpopulations, more consistent with the canonical cortical column architecture. It is shown that under both single- and multi-area simulations of event-related potentials (ERPs), FSM outperforms classic NMMs. In the second contribution, the DCM approach is used to provide insights into the underlying neural circuit dynamics of pattern reversal visual evoked potentials extracted from concurrent EEG-fMRI data. An optimal DCM model with recurrent forward-backward process disclosed the timing of signal propagation across ventral and dorsal connectivity pathways as well as the largescale effective connectivity in the human visual system. In the third contribution, an extension of GCM called 'partial' Granger causality (PGq is introduced to decipher the directed functional connectivity of ERPs. It is shown that time-domain PGC can detect the underlying causal connectivity relatively rapidly and robustly while capturing the accurate evolution of the directed neural connectivity dynamics over time. Lastly, PGC technique applied to EEG segments under a robot-assisted gait training reveals brain connectivity changes in fronto-centroparietal network with strong ·correlation with the behavioural performance of individuals.