All animals must cope with the challenges and the requirements constantly imposed by an ever-changing environment. To this end, a number of sensory modalities are continuously exploited in order to collect information about those aspects of the surrounding world which are critical for survival. For many species, vision is the dominant modality, and it is also the most studied, given its relevance for comparison with our own species. Moreover, many of the perceptual and cognitive processes developed during evolution are nothing but the result of hardwired principles underlying the organisation of nervous systems, and the visual subsystem plays a major role in this scenario. Memory processes and the formation of concepts are two among the cognitive functions that strongly depend on the contribution of visual information. The link between the evolution of signal processing and the formation of internal representations is a subject deserving accurate analysis, and special attention should be paid to those behavioural and neural processes that might provide hints on the emergence and nature of abstract rules in the minds of non-human animals. The spatial domain offers a very rich basis for venturing in such an exploration.State of current research A field of research which has provided important results concerns the representation of environmental space in the processes of animal learning. The ability to maintain a faithful memory trace of the relative position of places in the environment is an indisputable necessity for many species. This ability is at the basis of a number of highly adaptive behaviours, from the exploration far from the nest in search for food, to the territorial monitoring of potential predators. A mechanism commonly used by animals which use vision as the main sensory system, consists in the use of landmarks in order to orient in space. Many studies indicate that animals are able to construct relational representations of space based on the encoding in memory of distances and directions between objects present in the environment. Right in this frame are a number of research works carried out by myself and aimed at investigating the spatial memory and the generalization ability of a geometric concept: the centre. In the landscape of studies on the evolution of cognition, what appears still lacking is an empirical (but also a theoretical) junction between data concerning the structure of the perceived space (at the level of the visual input) and the mental representation of environmental space. Moreover, a general and evolutionary approach to this problem has scarcely appeared in the literature insofar, with one or two enlightening exceptions. More recently, the work by Roger Shepard has produced a number of laws describing the organisation of internal representations, which have an appeal for universality, in the sense that their applicability transcends the restricted domain of one or another modality, or of one or another species, and can be considered the best rendering of some ‘evolutionary stable’ cognitive phenomena expressed so far in mathematical language. Taking advantage of my experience in animal cognition and psychobiology, I will concentrate on some issues that have arisen from empirical work, in particular the relation between visual organisation and the formation of spatial representations and concepts, and most importantly their evolution and implementation in the nervous systems of organisms.