Casimir forces: from Au to time crystals

The Casimir effect, a fundamental manifestation of quantum vacuum fluctuations, has evolved from a curiosity between idealized metallic plates to a versatile probe of quantum and material properties in structured and time-dependent media. This review traces the progression of Casimir force research from its classical formulation in noble metals like gold (Au) to cutting-edge developments involving metamaterials and time crystals. Beyond surveying recent experimental and theoretical advances, we provide a unifying framework that bridges Casimir physics with essential solid-state principles—including band theory, dielectric response, and temporal periodicity—critical for understanding forces in real and engineered materials. Special attention is given to non-equilibrium and dynamically modulated systems, where time-periodic structures can profoundly alter vacuum-induced interactions. By synthesizing insights from quantum field theory and condensed matter physics, this review offers a comprehensive perspective on the rich interplay between quantum fluctuations, material response, and temporal symmetry breaking.