There are many space plasma physics problems that are both majorand unsolved, there are other problems for which the categorization of solved or unsolved depends on one's point of view, and there are still other problems that are well understood but unsolved in the sense that quantitative predictions cannot be made although the basic physics is known. The following discussion will, of necessity, be limited and selective. The nature of the Alfvénic turbulence in the solar wind remains a major unsolved mystery: Why is the power spectrum of this anisotropic, compressible, magnetofluid often Kolmogoroff-like, with a power spectral index close to the -5/3 value characteristic of normal fluids? What is the three-dimensional symmetry of the turbulence? Are the magnetic fields quasi-two-dimensional and stochastic, or have they been highly refracted by small velocity shears? What is the origin of the -1 slope of the energy containing scales? What is the relationship between the turbulent fields and the diffusion coefficients for energetic particle transport parallel and perpendicular to the ambient magnetic field? A general problem in turbulence research is the relationship between the fluid approximation and the kinetic physics that describes the dissipation and damping of fluctuations. There is still much to learn about solar flares, coronal mass ejections and magnetospheric substorms. Another major puzzle is how to quantitatively describe the interaction of the solar wind with the interstellar medium; a problem probably not amenable to solution using fluid equations.