Abstract: The studies from 1999 to now on dynamics of delayed systemsare reviewed in this paper. They concernmechanics, mechanical engineering, aeronautics and astronautics,ecology, biology, neural network, laser, electronics, informationtechnology, security communication, economics and so on. The typical methods and techniques are discaussed. It is shownthat the delayed systems are ubiquitous in nature and engineering. Many new problems and phenomena need to be studied and explored even for some simple and known oscillators when the effects of delays on systems are considered. Based on some existing problems in the studies, some topics for future studies are suggested, for examples, control strategies focused on delayed feedbacks, effects of combining delay with nonlinearities on systems, delay induced multiple bifurcations and complex dynamics in systems, computing models focused on net systems with delayed coupling of state variables and so on. These problems should be addressed since they do not occur in nonlinear systems without delays.