The computational work to perform particle advection‐based flow visualization techniques varies based on many factors, including number of particles, duration, and mesh type. In many cases, the total work is significant, and total execution time (“performance”) is a critical issue. This state‐of‐the‐art report considers existing optimizations for particle advection, using two high‐level categories: algorithmic optimizations and hardware efficiency. The sub‐categories for algorithmic optimizations include solvers, cell locators, I/O efficiency, and precomputation, while the sub‐categories for hardware efficiency all involve parallelism: shared‐memory, distributed‐memory, and hybrid. Finally, this STAR concludes by identifying current gaps in our understanding of particle advection performance and its optimizations.