Flow visualization is an important approach for understanding fluid dynamics simulations. This survey focuses on flow visualization algorithms that use “particle advection,” a process that displaces particles in a flow field. The performance of these algorithms can vary greatly based on a variety of factors including workload, solver type, underlying mesh type, and optimizations employed. That said, the relationship between these factors and actual execution time is often not well understood. In response, this survey aims to illuminate performance aspects. It considers a decision-making workflow for assessing whether or not a particle advection workload requires optimized approaches to complete within a time bound. This workflow requires considering workload properties, cost models, and possible optimizations, and each of these topics is surveyed. Further, special attention is paid to parallelism and especially parallelism on supercomputers, including portable performance. Overall, the survey identifies three key limitations in realizing the decision-making workflow: in cost estimation, in expected performance increases from using GPUs, and in expected performance increases from using distributed-memory parallel techniques. Finally, the survey contributes new ideas for how particle advection components relate and for translating particle advection workloads to a cost formulation, also contributes some nascent preliminary work addressing each of the three limitations.