This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its magnitude, and the physics of a small (and potentially nonzero) vacuum energy. The cosmological constant, originally introduced by Einstein to allow static solutions to his equations, was later found unnecessary with the discovery of the universe's expansion. However, recent observations suggest that the cosmological constant may play a significant role in the universe's dynamics. The cosmological constant is now understood as a measure of the vacuum energy density, which is the sum of various contributions, each much larger than the observed value. This discrepancy is known as the cosmological constant problem. The cosmological constant modifies Einstein's equations, leading to Friedmann equations that include the vacuum energy density. These equations allow for static solutions, but the universe's expansion has eliminated the need for such a solution. The cosmological constant can be interpreted as a vacuum energy, and its value is constrained by observations. The observed value of the cosmological constant is much smaller than theoretical predictions, leading to the cosmological constant problem. Cosmological observations, including those of Type Ia supernovae and the cosmic microwave background, provide constraints on the cosmological constant. These observations suggest that the universe is accelerating, indicating a positive cosmological constant. The cosmological constant problem remains one of the most significant unsolved problems in fundamental physics.This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its magnitude, and the physics of a small (and potentially nonzero) vacuum energy. The cosmological constant, originally introduced by Einstein to allow static solutions to his equations, was later found unnecessary with the discovery of the universe's expansion. However, recent observations suggest that the cosmological constant may play a significant role in the universe's dynamics. The cosmological constant is now understood as a measure of the vacuum energy density, which is the sum of various contributions, each much larger than the observed value. This discrepancy is known as the cosmological constant problem. The cosmological constant modifies Einstein's equations, leading to Friedmann equations that include the vacuum energy density. These equations allow for static solutions, but the universe's expansion has eliminated the need for such a solution. The cosmological constant can be interpreted as a vacuum energy, and its value is constrained by observations. The observed value of the cosmological constant is much smaller than theoretical predictions, leading to the cosmological constant problem. Cosmological observations, including those of Type Ia supernovae and the cosmic microwave background, provide constraints on the cosmological constant. These observations suggest that the universe is accelerating, indicating a positive cosmological constant. The cosmological constant problem remains one of the most significant unsolved problems in fundamental physics.