Line defects in CFTs: from magnets to Wilson lines

Line defects describe one-dimensional probes of a quantum field theory. Physically interesting examples can be found in different systems, ranging from condensed matter physics to gauge theories. In this talk, I will briefly review some recent results on the renormalization group approach to line defects in CFTs. I will then discuss some applications. In particular, I will discuss some interesting RG flows for Wilson lines in massless gauge theories, and their relation with an instability to screening by charged fields.