Populations of nonlocally coupled, identical limit cycle oscillators can lead to the peculiar chimera state, in which subpopulations of synchronized and unsynchronized oscillators coexist in localized spatial domains. We study the existence and robustness of chimera states in populations of simple, complex and chaotic oscillators, which are different forms of oscillation realizable in experiments. In the case of simple oscillation, we investigate the existence and robustness of chimera states under physically relevant constraints in our model such as time delay and frequency heterogeneity. We show for the first time that chimera states can be extended to the general setting of complex and chaotic oscillators, in particular, we find spiral wave chimera together with synchronization defect lines. We also introduce several methods for selecting parameters in general models that lead to the formation of chimera states in 1D or 2D systems, which can provide important theoretical guidance to future experimental studies.