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This paper reviews past research and new studies underway of the local interstellar environment and its changing influence on the heliosphere. The size, shape, and physical properties of the heliosphere outside of the heliopause are determined by the surrounding environment - now the outer region of the Local Interstellar Cloud (LIC). Analysis of high-resolution HST spectra led to a kinematic model with many interstellar clouds. This analysis identified fifteen clouds located within about 10 pc of the Sun and their mean temperatures, turbulence, and velocity vectors. With the increasing number of sight lines now being analyzed, we find that temperatures and turbulent velocities have spatial variations within the LIC and other nearby clouds much larger than measurement uncertainties, and that these spatial variations appear to be randomly distributed and can be fit by Gaussians. The inhomogeneous length scale is less than 4,000 AU, a distance that the heliosphere will traverse in less than 600 years. The temperatures and turbulent velocities do not show significant trends with stellar distance or angle from the LIC center. If/when the Sun enters an inter-cloud medium, the physical properties of the future heliosphere will be very different from the present. For the heliosheath and the very local interstellar medium (VLISM) just outside of the heliopause, the total pressures are approximately equal to the gravitational pressure of overlying material in the Galaxy. The internal pressure in the LIC is far below that in the VLISM, but there is an uncertain ram pressure term produced by the flow of the LIC with respect to its environment.