In this talk we will introduce Ulrich sheaves on algebraic varieties.
The story of those sheaves starts from module theoretical notions in the '80, but since the work of Eisenbud and Schreyer
in 2006 their geometric side has received many attentions.
We will explain the main properties of Ulrich sheaves under the weak assumption of an ample and globally generated polarization.
After some examples, the focus will be on Ulrich bundles on Fano $3$-folds of index $2$, explaining their construction
and some properties of the associated moduli spaces.
