The author investigates several spaces of harmonic functions, including Bloch, Hardy, weighted Bergman, Besov and Dirichlet spaces on the unit ball in \(\mathbb R^n\). The paper studies the relationships among the above spaces as well as equivalent conditions for harmonic Bergman and Besov spaces. Section 5 of the paper includes several results concerning harmonic functions whose homogeneous polynomial expansion has Hadamard gaps.