  This article deals with the asymptotic behaviour as $t\to +\infty$ of the
survival function $P[T > t],$ where $T$ is the first passage time above a non
negative level of a random process starting from zero. In many cases of
physical significance, the behaviour is of the type $P[T > t]=t^{-\theta +
o(1)}$ for a known or unknown positive parameter $\theta$ which is called a
persistence exponent. The problem is well understood for random walks or L\'evy
processes but becomes more difficult for integrals of such processes, which are
more related to physics. We survey recent results and open problems in this
field.
