Based on analyses of responses of insects and mites to a wide range of diel and nondiel experimental light-dark schedules, a variety of models have been developed for the photoperiodic clocks in these species by nearly as many investigators. According to some of these models, the photoperiodic clock is based on a mechanism separate from the circadian system, that is, a so-called "hourglass." According to other models, the clock is based on one or more circadian oscillators that may be coupled to each other and that may or may not show a certain degree of damping. In this context, a rapidly damping oscillator could be regarded as an hourglass. The present article gives an overview of the many different clock models and their philosophies, and it makes comparisons among them to provide a better understanding about how these models are related, if at all, and why the double circadian oscillator model is the most favored model at present.