The case for the cosmological constant

I present a short overview of current observational results and theoretical models for a cosmological constant. The main motivation for invoking a sma ll cosmological constant (or Lambda-term) at the present epoch has to do wi th observations of high redshift Type Ia supemovae which suggest an acceler ating universe. A flat accelerating universe is strongly favoured by combin ing supernovae observations with observations of CMB anisotropies on degree scales which give the 'best-fit' values Omega(Lambda) similar or equal to 0.7 and Omega(m) similar or equal to 0.3. A time dependent cosmological Lam bda-term can be generated by scalar field models with exponential and power law potentials. Some of these models can alleviate the 'fine tuning' probl em which faces the cosmological constant.