This review discusses several aspects of the cosmological constant both from the cosmological and field theoretical perspectives with the emphasis on conceptual and fundamental issues rather than on observational details. The plan of the review is as follows: This section introduces the key issues related to cosmological constant and provides a brief historical overview. (For previous reviews of this subject, from cosmological point of view, see [1, 2, 3, 138].) Section 2 summarizes the kinematics and dynamics of the standard Friedmann model of the universe paying special attention to features involving the cosmological constant. Section 3 reviews the observational evidence for cosmological constant, especially the supernova results, constraints from the age of the universe and a few others. We next study models with evolving cosmological `constant' from different perspectives. (In this review, we shall use the term cosmological constant in a generalized sense including the scenarios in which cosmological "constant" is actually varying in time.) A phenomenological parameterization is introduced in section 4.1 to compare theory with observation and is followed up with explicit models involving scalar fields in section 4.2. The emphasis is on quintessence and tachyonic scalar field models and the cosmic degeneracies introduced by them. Section 5 discusses cosmological constant and dark energy in the context of models for structure formation and section 6 describes the constraints arising from CMBR anisotropies.
The latter part of the review concentrates on more conceptual and fundamental aspects of the cosmological constant. (For previous reviews of this subject, from a theoretical physics perspective, see [4, 5, 6].) Section 7 provides some alternative interpretations of the cosmological constant which might have a bearing on the possible solution to the problem. Several relaxation mechanisms have been suggested in the literature to reduce the cosmological constant to the currently observed value and some of these attempts are described in Section 8. Section 9 gives a brief description of the geometrical structure of the de Sitter spacetime and the thermodynamics of the de Sitter universe is taken up in section 10. The relation between horizons, temperature and entropy are presented at one go in this section and the last section deals with the role of string theory in the cosmological constant problem.