We review the status of attempts to measure the present cosmological expans
ion rate No and to estimate the cosmological density parameters for neutrin
os baryons, nonrelativistic matter and vacuum energy. While the total densi
ty appears to have a 'reasonable' value near the critical density, the four
components have mysterious values that require an explanation from fundame
ntal physics. (C) 2000 Academie des sciences/Editions scientifiques et medi
cales Elsevier SAS.