The development of approaches to design and manufacture complex 3D functional mesoscopic structures in advanced materials is a topic of increasing research interest. Previous options in forming 3D mesostructures are, however, constrained by a narrow accessible range of materials or 3D geometries. In this talk, I will first introduce a versatile, mechanical approach to deterministically assemble sophisticated 3D mesoscale structures, guided by mechanics analysis, from planar 2D structures through controlled compressive buckling. To enhance the geometric diversity and functionality of 3D mesostructures, various mechanics-guided design strategies, for both the 2D precursor structures and the supporting substrates, will be demonstrated. Based on this mechanical assembly approach, many unique opportunities for 3D bio-integrated functional systems exist, for example, 3D multifunctional neural interfaces for cortical spheroids and 3D artificial microvascular networks. Precisely defined 3D geometries and deterministically distributed functional components through well-defined volumetric spaces, for unconventional approaches to neuromodulation, sensing, and regulation, highlight the design versatility driven by mechanics analysis. I will also briefly present a soft, shape-programmable system that exploits liquid metal microfluidic networks embedded in an elastomer matrix, with electromagnetic forms of actuation, to achieve a unique set of properties. Key features include fast and continuous surface shape morphing and reprogramming with access to a diverse set of 3D shapes originating from a single 2D planar configuration and well-controlled 4D (spatiotemporal) electronic programmability. Mechanics methods capable of precisely predicting complex 3D surface shape transformations in non-uniform magnetic fields serve as the design tool for various 3D target shapes.