Recent dramatic acceleration, thinning and retreat of tidewater outlet glaciers in Greenland raises concern regarding their contribution to future sea-level rise. These dynamic changes seem to be parallel to oceanic and climatic warming but the linking mechanisms and forcings are poorly understood and, furthermore, large-scale ice sheet models are currently unable to realistically simulate such changes which provides a major limitation in our ability to predict dynamic mass losses. In this paper we apply a specifically designed numerical flowband model to Jakobshavn Isbrae (JIB), a major marine outlet glacier of the Greenland ice sheet, and we explore and discuss the basic concepts and emerging issues in our understanding and modelling ability of the dynamics of tidewater outlet glaciers. The modelling demonstrates that enhanced ocean melt is able to trigger the observed dynamic changes of JIB but it heavily relies on the feedback between calving and terminus retreat and therefore the loss of buttressing. Through the same feedback, other forcings such as reduced winter sea-ice duration can produce similar rapid retreat. This highlights the need for a robust representation of the calving process and for improvements in the understanding and implementation of forcings at the marine boundary in predictive ice sheet models. Furthermore, the modelling uncovers high sensitivity and rapid adjustment of marine outlet glaciers to perturbations at their marine boundary implying that care should be taken in interpreting or extrapolating such rapid dynamic changes as recently observed in Greenland.