The case for a positive cosmological Lambda-term

Recent observations of Type 1a supernovae indicating an accelerating univer se have once more drawn attention to the possible existence, at the present epoch, of a small positive Lambda-term (cosmological constant). In this pa per we review both observational and theoretical aspects of a small cosmolo gical Lambda-term. We discuss the current observational situation focusing on cosmological tests of Lambda including the age of the universe, high red shift supernovae, gravitational lensing, galaxy clustering and the cosmic m icrowave background. We also review the theoretical debate surrounding Lamb da: the generation of Lambda in models with spontaneous symmetry breaking a nd through quantum vacuum polarization effects - mechanisms which are known to give rise to a large value of Lambda hence leading to the "cosmological constant problem." More recent attempts to generate a small cosmological c onstant at the present epoch using either field theoretic techniques, or by modelling a dynamical Lambda-term by scalar fields are also extensively di scussed. Anthropic arguments favouring a small Lambda-term are briefly revi ewed. A comprehensive bibliography of recent work on Lambda is provided.