Survey on some aspects of Lefschetz theorems in algebraic geometry

We survey classical material around Lefschetz theorems for fundamental groups, and show the relation to parts of Deligne's program in Weil II. The notes are based on some aspects of the material for the Santal\'o lectures at the Universidad Complutense de Madrid (October 2015) and the Rademacher lectures at the University of Pennsylvania (February 2016). They appear in Revista Matem\'atica Complutense.