  These are the notes for a minicourse taught at the 2022 ICTP summer school
`Frontiers in Geometry and Topology'. The goal is to introduce families of
Dirac operators and how they can be used to study interactions between geometry
and topology. In particular, we discuss the index theorem for families of
twisted Dirac operators, and its applications to metrics of positive scalar
curvature and the three-dimensional Weinstein conjecture.
