Perspective cameras are the most popular imaging sensors used in computer vision. However, many application fields, including automotive, surveillance, and robotics, require the use of wide angle cameras (e.g., fisheye), which allow to acquire a larger portion of the scene using a single device at the cost of the introduction of noticeable radial distortion in the images. Affine covariant feature detectors have proved successful in a variety of computer vision applications, including object recognition, image registration, and visual search. Moreover, their robustness to a series of variabilities related to both the scene and the image acquisition process has been thoroughly studied in the literature. In this paper, we investigate their effectiveness on fisheye images providing both theoretical and experimental analyses. As theoretical outcome, we show that the inherently non-linear radial distortion can be locally approximated by linear functions with a reasonably small error. The experimental analysis builds on Mikolajczyk's benchmark to assess the robustness of three popular affine region detectors (i.e., maximally stable extremal regions, and Harris and Hessian affine region detectors), with respect to different variabilities as well as to radial distortion. To support the evaluations, we rely on the Oxford data set and introduce a novel benchmark data set comprising 50 images depicting different scene categories. Experiments are carried out on rectilinear images to which radial distortion is artificially added, and on real-world images acquired using fisheye lenses. Our analysis points out that affine region detectors can be effectively employed directly on fisheye images and that the radial distortion is locally modeled as an additional affine variability.