We review the findings for the values of the cosmological parameters as derived from high-redshift SNIa measurements .
The most recent results confirm the picture of a non-empty inflationary Universe that is consistent with a cosmological constant \Omega _ { \Lambda } \simeq 0.7 .
This implies that the expansion of the Universe is currently accelerated by the action of some mysterious dark energy .
We also discuss the possibility and the consequences of the fact that SNIa may not be perfect standard candles , in the sense of having properties in the early Universe that are systematically different from those they have at the present times .