With very few exceptions, almost all models describing the interaction of the solar wind with the local interstellar medium (LISM) are essentially steady-state. However, the solar wind ram pressure varies on an 11 year solar cycle period, and the solar wind is traversed by numerous shock waves. It has long been recognized that variation in the solar wind ram pressure can move the termination shock inward and outward on a complementary time scale. We describe here the variation in global heliospheric structure in response to a solar cycle variation in the ram pressure. The models include interstellar neutral hydrogen self-consistently. Also described is the role of ion-neutral friction in driving a “Rayleigh-Taylor-like” instability in the vicinity of the heliospheric nose.