We develop monotonically convergent algorithms for solving typical quantum optimal control problems in chemistry and physics. They include (1) state-to-state control for a system nonlinearly interacting with a control and (2) operator pulse design under the influence of dissipation. We discuss the solution algorithms in a unified manner. As an application of the first algorithm, we consider the alignment/orientation control of diatomic molecules. The alignment is achieved through the polarizability coupling between shaped laser pulses and molecules. When the retaining of the aligned state is chosen as a physical objective, the control pulse is shown to utilize the so-called "coherent destruction of tunneling" mechanisms. This numerical observation is confirmed by using a simple analytical model. Second application is associated with (2). In quantum information processing and quantum computer, the realization of gate operations in physical systems is essential. As the operations should be done with quite high precision, optimal control approaches could be suitable tools for this purpose. We discuss the possibility through case studies such as quantum algorithm simulations and suppression of decoherence.