In classical 3-manifold topology, a Heegaard splitting of a 3-manifold $M$ is a decomposition of $M$ into a union of two handlebodies that meet along a surface. A Heegaard splitting gives rise to an accompanying Heegaard diagram, which conversely gives instructions for reconstructing $M$. Every 3-manifold can be obtained from one of these pictures, which in some ways reduces the study of 3-manifolds to the combinatorics of these diagrams.

In 2012, Gay and Kirby introduced the notion of a trisection of a closed 4-manifold $X$, which is a decomposition of $X$ into three 4-dimensional handlebodies that intersect nicely. Trisections exhibit many similarities to Heegaard splittings; in particular, a trisected 4-manifold corresponds to a trisection diagram.

In this talk I will define Heegaard splittings and trisections and give as many examples (including colorful pictures) as possible.