Recent progress in soft material chemistry and enabling methods of 3D and 4D fabrication—emerging programmable material designs and associated assembly methods for the construction of complex functional structures—is highlighted. The underlying advances in this science allow the creation of soft material architectures with properties and shapes that programmably vary with time. The ability to control composition from the molecular to the macroscale is highlighted—most notably through examples that focus on biomimetic and biologically compliant soft materials. Such advances, when coupled with the ability to program material structure and properties across multiple scales via microfabrication, 3D printing, or other assembly techniques, give rise to responsive (4D) architectures. The challenges and prospects for progress in this emerging field in terms of its capacities for integrating chemistry, form, and function are described in the context of exemplary soft material systems demonstrating important but heretofore difficult-to-realize biomimetic and biologically compliant behaviors.