Astronomy and Space Domain Awareness are limited by the size of available telescope optics, the cost for which scales steeply due to the exquisitely ground and polished primary mirrors, typically made of glass or other lightweight substrates. Liquid mirrors (LMs) may break this unfavorable cost scaling. When rotated at a constant angular velocity, it has been shown that fluid surfaces take the form of a paraboloid, which can function as a primary mirror. However, current LMs cannot slew or tilt off-zenith due to gravity, greatly limiting the viewing area in the sky. To overcome these limitations while also enabling low-cost, very-large-aperture telescopes, the Defense Advanced Research Projects Agency launched the Zenith program. Zenith is developing entirely new LM design-for-build approaches that can create large optical surfaces without rotation and maintain the optical quality during tilt and slew by correcting transient liquid surface aberrations in real time. The development of these new designs is being supported by multi-physics models, materials, surface and field controls, and structures. We discuss key and fundamental aspects of four new design and modeling approaches for this new class of LMs, and the software and simulation tools developed by the Zenith program to design tiltable and size-scalable liquid mirrors.