Our recent theoretical and/or Monte Carlo results for dilute solution properties of semiflexible ring polymers on the basis of the wormlike ring model are briefly summarized. The behavior of the mean-square radius of gyration , intrinsic viscosity [eta], scattering function P(k) with k the magnitude of the scattering vector, and second virial coefficient A(2,Theta) at the Theta state is examined as a function of the reduced contour length lambda L, where lambda(-1) and L are the stiffness parameter and contour length of the wormlike ring, respectively. Effects of the topological constraints on , [eta] P(k), and A(2,Theta) of semiflexible rings are also examined by comparing the results for the wormlike rings without the topological constraints with those for the wormlike ring of the trivial or trefoil knot.