  A family $\mathcal{A}$ of sets is said to be \emph{$t$-intersecting} if any
two sets in $\mathcal{A}$ have at least $t$ common elements. A central problem
in extremal set theory is to determine the size or structure of a largest
$t$-intersecting sub-family of a given family $\mathcal{F}$. We give a survey
of known results, conjectures and open problems for various important families
$\mathcal{F}$, namely, power sets, levels of power sets, hereditary families,
families of signed sets, families of labeled sets, and families of
permutations. We also provide some extensions and consequences of known
results.
