As quantum chemistry plays a more and more central role in many complicated chemical problems, it has become necessary to obtain accurate results for large molecular systems. Conventional quantum chemistry methods are either too expensive to apply to large systems or too approximate for the results to be reliable, and they fail to satisfy this requirement. A variety of different approaches is being developed with the aim of achieving this goal: local correlation methods; divide–and–conquer methods; linear–scaling density functional methods based on the fast multipole and other approximations; effective potential methods; and hybrid methods. ONIOM (our N–layered integrated molecular orbital plus molecular mechanics method), developed by the authors, is a hybrid method in which a large molecular system is divided into onion–skin–like layers, and different quantum chemistry/molecular mechanics methods are used for different parts of the system; the results are combined to extrapolatively estimate the results of high–level calculation for the real system. Several applications of ONIOM will be discussed.