The article provides a comprehensive review of both new experimental and theoretical advancements in the Casimir effect. The Casimir effect, a quantum phenomenon, arises from the zero-point electromagnetic energy altered by boundaries, resulting in a force that can be attractive or repulsive depending on the geometry and topology of the boundary. The review covers the general structure of divergences in field theory, the use of zeta-functional regularization and heat kernel expansion to remove these divergences, and different representations for the regularized vacuum energy. It discusses the Casimir energies and forces in various configurations, including stratified media, rectangular cavities, spheres, and cylinders, and explores the effects of nonzero temperature, finite conductivity, and surface roughness. The article also reviews modern precision experiments on measuring the Casimir force, comparing their results with theoretical predictions, and discusses the constraints on non-Newtonian gravitational laws and other long-range interactions derived from Casimir force measurements. The review is structured to be accessible to specialists in different fields of physics and students, with detailed calculations and examples provided for clarity.The article provides a comprehensive review of both new experimental and theoretical advancements in the Casimir effect. The Casimir effect, a quantum phenomenon, arises from the zero-point electromagnetic energy altered by boundaries, resulting in a force that can be attractive or repulsive depending on the geometry and topology of the boundary. The review covers the general structure of divergences in field theory, the use of zeta-functional regularization and heat kernel expansion to remove these divergences, and different representations for the regularized vacuum energy. It discusses the Casimir energies and forces in various configurations, including stratified media, rectangular cavities, spheres, and cylinders, and explores the effects of nonzero temperature, finite conductivity, and surface roughness. The article also reviews modern precision experiments on measuring the Casimir force, comparing their results with theoretical predictions, and discusses the constraints on non-Newtonian gravitational laws and other long-range interactions derived from Casimir force measurements. The review is structured to be accessible to specialists in different fields of physics and students, with detailed calculations and examples provided for clarity.