It has been known for half a century that the interstellar medium (ISM) of our Galaxy is structured on scales as small as a few hundred km, more than 10 orders of magnitude smaller than typical ISM structures and energy input scales. In this review we focus on neutral and ionized structures on spatial scales of a few to ~10^4 Astronomical Units (AU) which appear to be highly overpressured, as these have the most important role in the dynamics and energy balance of interstellar gas: the Tiny Scale Atomic Structure (TSAS) and Extreme Scattering Events (ESEs) as the most over-pressured example of the Tiny Scale Ionized Structures (TSIS). We review observational results and highlight key physical processes at AU scales. We present evidence for and against microstructures as part of a universal turbulent cascade and as discrete structures, and review their association with supernova remnants, the Local Bubble, and bright stars. We suggest a number of observational and theoretical programs that could clarify the nature of AU structures. TSAS and TSIS probe spatial scales in the range of what is expected for turbulent dissipation scales, therefore are of key importance for constraining exotic and not-well understood physical processes which have implications for many areas of astrophysics. The emerging picture is one in which a magnetized, turbulent cascade, driven hard by a local energy source and acting jointly with phenomena such as thermal instability, is the source of these microstructures.
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