Today, both military and civilian applications require miniaturized and cheap optical systems. To reduce their size and their mass, imaging systems have to be as simple as possible, which means that they have to involve a minimal number of optical elements. The simplest system can be defined as a system which is composed of only three elements: a single optical component, an aperture stop and a detector. However, these elements can be complex if needed: for instance, curved detector, optics with aspheric surfaces or diffractive optical elements, microlens array with a complex shape... This paper aims at presenting the range of optical architectures available for a simple system. Thanks to the formalism of third-order Seidel aberrations, several strategies of simplification and miniaturization of optical systems are examined. This approach leads to a classification of existing miniaturized imaging systems which are described in literature (such as multichannel systems). Figures of merit are also introduced to assess the performance capabilities of such systems, showing the necessary trade-off between simplicity, miniaturization, and optical performance.