Arguments favouring > 0 at the present epoch essentially stem from four sets of observations:
(i) The age issue: A high value of the Hubble constant H0 ~ 80 km/sec/Mpc predicts a short age of the universe which is incompatible with the ages of the oldest stars (12 - 16 Gyr) unless the universe is open (m < 0.1) or flat and dominated m + = 1. The appeal of this argument has somewhat decreased following recent Hipparcos parallax measurements indicating a lower value H0 67 km/sec/Mpc and also a lower age for globular clusters: 11.5 ± 1.5 Gyr. Still, recent observations of old galaxies at high redshifts are extremely difficult to accommodate within the framework of a flat matter dominated cosmology unless the Hubble parameter is very small (H0 45 km/sec/Mpc; section 4.1).
(ii) Structure formation: The standard COBE normalized cold dark matter model of structure formation with m = 1 appears to be in serious conflict with observations. The situation may be remedied if the universe is flat, with most of matter smoothly distributed in the form of a cosmological constant and only a small fraction m h 0.2 in clustered matter. (Here h is the Hubble constant in units of 100 km/s/Mpc). Studies of the abundance and evolution of clusters of galaxies and of lensing by clusters also appear to favour a low density universe (section 4.6).
(iii) Baryon excess in clusters: In a spatially flat universe with m = 1 the mass fraction in baryons in the Coma cluster is expected to greatly exceed nucleosynthesis bounds leading to what has been called the `baryon catastrophe'. The mass fraction in baryons can be kept in agreement with nucleosynthesis constraints only if m h 0.16  (m includes contribution from baryons and clustered dark matter). Agreement with the Inflationary scenario which strongly favours a spatially flat universe then suggests that the remaining mass might be in the form of a cosmological constant.
(iv) High redshift supernovae and the cosmic microwave background: Preliminary results from this rapidly advancing field of cosmology suggest that the universe may be accelerating universe with a dominant contribution to its energy density coming in the form of cosmological -term. These results, when combined with CMB anisotropy observations on intermediate angular scales, strongly support a flat universe m + = 1 with ~ 0.6 - 0.7 (sections 4.3 & 4.4).
In the first half of this paper we shall briefly review the present observational status of the cosmological constant referring the reader to the original papers and earlier reviews [26, 37] for more details.