Over these three lectures we will discuss a few different ideas that come together to yield an example of a finite-time singularity for the 3d Euler equation. The first lecture will be a discussion of the Biot-Savart law, which encodes the nonlocal nature of the Euler equation. In the second lecture we will discuss the concept of self-similarity in some blow-up problems, particularly in 1d models of the Euler equation. In the third lecture we will discuss how to apply some of these ideas to the simplest scenario where a blow-up is possible in the 3d Euler equation. Different aspects of the talks will take from previous works joint with In-Jee Jeong, Tej Ghoul, and Nader Masmoudi.