This article provides a comprehensive review of the physics and cosmology of the cosmological constant, focusing on recent developments. It begins by discussing the historical context of the cosmological constant, originally introduced to allow static solutions to Einstein's equations, and its subsequent role in explaining various observations. The author highlights the puzzle of why the observed vacuum energy is so much smaller than the scales of particle physics, known as the "cosmological constant problem." The article then delves into the modern understanding of the cosmological constant as a measure of the energy density of the vacuum, which can be derived from various contributions, including potential energies from scalar fields and zero-point fluctuations. These contributions are typically much larger than the observed value, leading to the cosmological constant problem. The review also covers the implications of a cosmological constant on the evolution of the universe, including the behavior of universes dominated by matter and vacuum energy. It discusses the dynamics of universes with different combinations of matter density and vacuum energy, and the conditions under which the universe expands forever or recollapses. Observational tests, such as Type Ia supernovae and cosmic microwave background (CMB) data, are presented as crucial evidence for the existence of a positive cosmological constant. The supernova results indicate an accelerating universe, while CMB data provides constraints on the spatial curvature and matter density of the universe. Finally, the article explores the potential impact of a cosmological constant on large-scale structure formation, noting that it can suppress the growth of perturbations. The review concludes by emphasizing the ongoing efforts to better understand the cosmological constant and its role in the universe.This article provides a comprehensive review of the physics and cosmology of the cosmological constant, focusing on recent developments. It begins by discussing the historical context of the cosmological constant, originally introduced to allow static solutions to Einstein's equations, and its subsequent role in explaining various observations. The author highlights the puzzle of why the observed vacuum energy is so much smaller than the scales of particle physics, known as the "cosmological constant problem." The article then delves into the modern understanding of the cosmological constant as a measure of the energy density of the vacuum, which can be derived from various contributions, including potential energies from scalar fields and zero-point fluctuations. These contributions are typically much larger than the observed value, leading to the cosmological constant problem. The review also covers the implications of a cosmological constant on the evolution of the universe, including the behavior of universes dominated by matter and vacuum energy. It discusses the dynamics of universes with different combinations of matter density and vacuum energy, and the conditions under which the universe expands forever or recollapses. Observational tests, such as Type Ia supernovae and cosmic microwave background (CMB) data, are presented as crucial evidence for the existence of a positive cosmological constant. The supernova results indicate an accelerating universe, while CMB data provides constraints on the spatial curvature and matter density of the universe. Finally, the article explores the potential impact of a cosmological constant on large-scale structure formation, noting that it can suppress the growth of perturbations. The review concludes by emphasizing the ongoing efforts to better understand the cosmological constant and its role in the universe.