It is well known that a Bernstein-Greene-Kruskal (BGK) mode can be easily constructed as an exact nonlinear solution of the one dimensional Vlasov-Poisson equation for a plasma. BGK modes have been used to explain electrostatic structures observed in space. However, some three dimensional (3D) features were also observed in these structures. For a long time, there has not been much effort in trying to construct exact 3D or 2D BGK modes. A solution for an infinitely strong magnetic field case has been constructed under the guiding center approximation, but there have been questions about the existence of solutions in a 3D unmagnetized plasma. We showed recently for such case that a spherically symmetric solution can indeed be constructed if it depends on energy as well as angular momentum. We have also constructed 2D BGK modes with cylindrical symmetry for the case with a finite magnetic guide field. Some comparisons with observations will be shown.