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A common approach to modeling kinetic problems in plasma physics is to represent the plasma as a set of Lagrangian macro-particles which interact through long-range forces. In the well-known particle-in-cell (PIC) method, the particle charges are interpolated to a mesh and the fields are obtained using a fast Poisson solver. The advantage of this approach is that the electrostatic forces can be evaluated in time O(N log N), where N is the number of macro-particles, but the scheme has difficulty resolving steep gradients and handling nonconforming domains unless a sufficiently fine mesh is used. The current work describes a grid-free alternative, the boundary integral/treecode (BIT) method. Using Green's theorem, we express the solution to Poisson's equation as the sum of a volume integral and a boundary integral which are computed using particle discretizations. The treecode replaces particle-particle interactions by particle-cluster interactions which are evaluated by Taylor expansions. In addition, the Green's function is regularized and adaptive particle insertion is implemented to maintain resolution. Like PIC, the operation count is O(N log N), but BIT avoids using a regular grid, so it can potentially resolve steep gradients and handle complex domains more efficiently. We applied BIT to several bounded plasma problems including a one-dimensional (1-D) sheath in direct current (dc) discharges, 1-D virtual cathode, cold two-stream instability, two-dimensional (2-D) planar and cylindrical ion optics, and particle dynamics in a Penning-Malmberg trap. Some comparisons of BIT and PIC were performed. These results and ongoing work will be reviewed. [ABSTRACT FROM AUTHOR]