  Broadly speaking, twistor theory is a framework for encoding physical
information on space-time as geometric data on a complex projective space,
known as a twistor space. The relationship between space-time and twistor space
is non-local and has some surprising consequences, which we explore in these
lectures. Starting with a review of the twistor correspondence for
four-dimensional Minkowski space, we describe some of twistor theory's historic
successes (e.g., describing free fields and integrable systems) as well as some
of its historic shortcomings. We then discuss how in recent years many of these
problems have been overcome, with a view to understanding how twistor theory is
applied to the study of perturbative QFT today. These lectures were given in
2017 at the XIII Modave Summer School in mathematical physics.
