The paper by Varun Sahni and Alexei Starobinsky reviews the observational and theoretical aspects of a small positive cosmological constant (Λ-term) in the context of an accelerating universe. Recent observations of Type Ia supernovae suggest that the universe is accelerating, leading to the possibility of a non-zero Λ-term. The authors discuss various observational tests of Λ, including the age of the universe, high-redshift supernovae, gravitational lensing, galaxy clustering, and the cosmic microwave background (CMB). They also explore theoretical mechanisms for generating a small Λ-term, such as spontaneous symmetry breaking and quantum vacuum polarization effects. The paper highlights the "cosmological constant problem," which is the discrepancy between the predicted and observed values of Λ. Recent attempts to generate a small Λ-term using field-theoretic techniques or dynamical scalar fields are discussed. The paper concludes with a comprehensive bibliography on recent work related to the cosmological constant.The paper by Varun Sahni and Alexei Starobinsky reviews the observational and theoretical aspects of a small positive cosmological constant (Λ-term) in the context of an accelerating universe. Recent observations of Type Ia supernovae suggest that the universe is accelerating, leading to the possibility of a non-zero Λ-term. The authors discuss various observational tests of Λ, including the age of the universe, high-redshift supernovae, gravitational lensing, galaxy clustering, and the cosmic microwave background (CMB). They also explore theoretical mechanisms for generating a small Λ-term, such as spontaneous symmetry breaking and quantum vacuum polarization effects. The paper highlights the "cosmological constant problem," which is the discrepancy between the predicted and observed values of Λ. Recent attempts to generate a small Λ-term using field-theoretic techniques or dynamical scalar fields are discussed. The paper concludes with a comprehensive bibliography on recent work related to the cosmological constant.