We review the recent progress in the study of magnetic materials using a high-frequency electron spin-resonance (ESR) technique. First, we show how useful high-frequency ESR is for studying antiferromagnetic materials, where the ESR frequency and magnetic field depend greatly on the exchange interaction and anisotropy energy of the materials. Next, we review the recent high-frequency ESR experiments made on spin S = 1 quasi-one-dimensional Heisenberg antiferromagnets (Q1D HAFs) and the spin-Peierls system CuGeO3. Then, we review the ESR studies performed on more complex systems, such as an S = 1 Q1D HAF with bond alternation, spin-ladder compounds and quasi-two-dimensional magnets. Each of these systems has a singlet ground state of quantum origin and an energy gap to the lowest excited state. On applying an external magnetic field, these systems show a transition from the non-magnetic to a magnetized state, and in some cases, long-range magnetic ordering occurs. Efforts are made to explain the underlying physics intuitively at the expense of rigour.