An experimental investigation of the structure of identified quark and gluon jets is presented. Observables related to both the global and internal structure of jets are measured; this allows for tests of QCD over a wide range of transverse momentum scales. The observables include distributions of jet-shape variables, the mean and standard deviation of the subjet multiplicity distribution and the fragmentation function for charged particles. The data are compared with predictions of perturbative QCD as well as QCD-based Monte Carlo models. In certain kinematic regions the measurements are sensitive mainly to perturbatively calculable effects, allowing for a test of QCD. The comparisons are also extended into regions where nonperturbative effects become large, and in this way the transition from hard to soft QCD is investigated. It is found that by including leading and next-to-leading logarithmic contributions in the QCD predictions, the agreement with the data can be extended to lower transverse momentum scales, especially for gluon jets.