The Sun, driving a supersonic solar wind, cuts out of the local interstellar medium a giant plasma bubble, the heliosphere. ESA, jointly with NASA, has had an important role in the development of our current understanding of the Suns' immediate neighborhood. Ulysses is the only spacecraft exploring the third, out-of-ecliptic dimension, while SOHO has allowed us to better understand the influence of the Sun and to image the glow of interstellar matter in the heliosphere. Voyager 1 has recently encountered the innermost boundary of this plasma bubble, the termination shock, and is returning exciting yet puzzling data of this remote region. The next logical step is to leave the heliosphere and to thereby map out in unprecedented detail the structure of the outer heliosphere and its boundaries, the termination shock, the heliosheath, the heliopause, and, after leaving the heliosphere, to discover the true nature of the hydrogen wall, the bow shock, and the local interstellar medium beyond. This will greatly advance our understanding of the heliosphere that is the best-known example for astrospheres as found around other stars. Thus, IHP/HEX will allow us to discover, explore, and understand fundamental astrophysical processes in the largest accessible plasma laboratory, the heliosphere.