  Recent cosmological observations suggest the existence of a positive
cosmological constant $\Lambda$ with the magnitude $\Lambda(G\hbar/c^3) \approx
10^{-123}$. This review discusses several aspects of the cosmological constant
both from the cosmological (sections 1-6) and field theoretical (sections 7-11)
perspectives. The first section introduces the key issues related to
cosmological constant and provides a brief historical overview. This is
followed by a summary of 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. Theoretical models (quintessence,
tachyonic scalar field, ...) with evolving cosmological `constant' are
described from different perspectives in the next section. Constraints on dark
energy from structure formation and from CMBR anisotropies are discussed in the
next two sections. The latter part of the review (sections 7-11) concentrates
on more conceptual and fundamental aspects of the cosmological constant.
Section 7 provides some alternative interpretations of the cosmological
constant which could 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. Next section 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 last section deals with
the role of string theory in the cosmological constant problem.
