Abstract The visual exploration of a scene involves the in- terplay of several competing processes (for example to se- lect the next saccade or to keep fixation) and the integration of bottom-up (e.g. contrast) and top-down information (the target of a visual search task). Identifying the neural mech- anisms involved in these processes and in the integration of these information remains a challenging question. Visual attention refers to all these processes, both when the eyes remain fixed (covert attention) and when they are moving (overt attention). Popular computational models of visual attention consider that the visual information remains fixed when attention is deployed while the primates are executing around three saccadic eye movements per second, changing abruptly this information. We present in this paper a model relying on neural fields, a paradigm for distributed, asyn- chronous and numerical computations and show that covert and overt attention can emerge from such a substratum. We identify and propose a possible interaction of four elemen- tary mechanisms for selecting the next locus of attention, memorizing the previously attended locations, anticipating the consequences of eye movements and integrating bottom- up and top-down information in order to perform a visual search task with saccadic eye movements.