Chain conformations and the presence of chain overlaps and entanglements in dilute polymer solutions have been analyzed. The fundamental problem of existence of chain overlaps in dilute solutions is related to the drag reduction phenomenon (DR). Even though DR occurs in solutions with the concentration of only few parts per million (ppm), some theories suggest that entanglements may play an important role in DR mechanism. Brownian dynamics technique have been used to perform simulations of dilute polymer solutions at rest and under shear flow. A measure of interchain contacts and two different measures of entanglements have been devised to evaluate the structure of polymer chains in solution. Simulation results have shown that overlaps and entanglements do exist in static dilute solutions as well as in solutions under shear flow. The effect of solution concentration, shear rate and molecular mass have been examined. In agreement with the solvation theory of DR mechanism, simulation results have demonstrated the importance of polymer + polymer interactions in dilute solutions.