The performances of several multireference electronic structure methods including complete active space self-consistent field (CASSCF)-based second-order perturbation theory (CASPT2), multireference configuration interaction with single and double excitations (MR-CISD), MR-CISD with the Davidson correction (MR-CISD+Q), and the CASSCF-based block-correlated coupled cluster method (CAS-BCCC4) we developed recently are compared by applying them to study several different chemical problems involving computation of ground state potential energy surfaces, the singlet-triplet gaps in diradicals, reaction barriers, and the excitation energies of low-lying excited states. Comparison with the results from other highly accurate theoretical methods or the available experimental data demonstrate that for all the problems studied, the overall performance of CAS-BCCC4 is competitive with that of MR-CISD+Q, and better than that of CASPT2 and MR-CISD methods. Thus the CAS-BCCC4 approach is expected to be a promising theoretical method for quantitative descriptions of the electronic structures of molecules with noticeable multireference character. multireference, block correlated coupled cluster, CASPT2, MR-CISD