The interstellar medium in the vicinity of the Sun is arranged in large-scale structures of bubble walls, sheets, and filaments of warm gas, within which close to the midplane there are subsheets and filaments of cold dense material; the whole occupies roughly half the available volume and extends with decreasing mean density to at least a kiloparsec off the plane. The remainder of the volume is in bubble interiors, cavities, and tunnels of much lower density, with some but not all of those lower density regions hot enough to be observable via their X-ray emission. This entire system is pervaded by a rather strong and irregular magnetic field and cosmic rays, the pressures of which are confined by the weight of the interstellar gas, particularly that far from the plane where gravity is strong. Observations suggest that the cosmic rays and magnetic field have an even more extended vertical distribution than the warm gas, requiring either the weight of additional coronal material or magnetic tension to confine it to the disk. Adjusting one's perception of this medium to embrace the known aspects is difficult. After this adjustment, there are many problems to solve and prejudices to overcome the weak role of thermal instability, the suppression of certain gravitational instabilities, the problem of determining the state in the low-density regions, the twin difficulties of not having too much OVI (O+5) and getting enough diffuse 3/4 keV X-ray emission, the possible importance of large old-barrel shaped supernova remnants in clarifying matters, the possible role of dust evolution in adjusting the heating to make clouds stable, the factors influencing the magnitudes of the interstellar pressure and scale height things that global models of the medium might examine to clarify some of these matters; attention to these details and more constitute the challenge of this subject.