An overview is given of the current state of theory and modelling for the interaction between the solar wind and the interstellar medium (ISM). The final frontiers of the solar wind, as it pushes itself into the ISM, have been an object of speculation and analysis for many years. Observational evidence from the solar wind and heliospheric energetic particles, and measurements of the very local interstellar medium (VLISM), have led to a consensus view of an inner termination shock, a heliopause, and, probably, a heliospheric bow shock. Within this straightforward description lie several issues of basic principle, for example the acceleration of interstellar pick-up ions and their relationship to the anomalous cosmic ray component, as well as more speculative issues such as temporal variations due to solar wind and VLISM inhomogeneities. The exciting prospect of the in situ detection of the heliospheric boundaries will be discussed.