Particle advection, the tracing of massless particles through a vector field, is a core technique for visualizing fluid flows. The resulting field lines, also called streamlines and pathlines, reveal the direction of the flow as well as features such as vortices. When dealing with large-scale flow fields, parallel methods must be used for particle advection. Field lines are difficult to scale in parallel, though, because of high load-imbalance and demanding communication and I/O overhead. In this talk, I will discuss two methods for advecting particles in large-scale flow fields. The first technique is designed to create a load-balanced data partitioning for parallel streamline computation. A graphical representation of the flow field, called a flow graph, is created to help estimate the workload of each data block. The second method is concerned with computing a series of Finite-Time Lyapunov Exponent Fields (FTLE) in parallel, which requires advecting massive numbers of pathlines in a time-varying flow field. By separating all available processes into different groups and forming a pipeline of process groups, faster computation times and less I/O overhead is achieved.