\def \smf@volume{}
\def \smf@fascicule{}
\def \@isbn{}
\def \@issn{}
\def \@precfile{}
\def \smf@firstpage{}
\def \smf@lastpage{21}
\def \smf@authors{Emmanuel Peyre}
\def \smf@shortauthors{Emmanuel Peyre}
\def \smf@langue{english}
\def \smf@title{Counting points on varieties\\using universal torsors}
\def \smf@shorttitle{Counting points using universal torsors}
\def \smf@ftitre{}
\def \smf@etitre{Counting points on varieties\\using universal torsors}
\def \smf@resume{}
\def \smf@abstract{ Around 1989, Manin initiated a program toward the understanding of the asymptotic behaviour of the rational points of bounded height on Fano varieties. This program led to the search of new methods to estimate the number of points of bounded height on various classes of varieties. Methods based on harmonic analysis were very successfull for compactifications of homogeneous spaces. However, they do not apply to other types of varieties. Universal torsors which were introduced by Colliot-Th\'el\`ene and Sansuc in connection with the Hasse principle and the weak approximation turned out to be a useful tool to attack other varieties. The aim of this short survey is to describe how it has been used in various simple examples. }