The present Thesis explored spatial reorientation behaviour of three species of fish (the zebrafish Danio rerio, the redtail splitfin fish Xenotoca eiseni, the goldfish Carassius auratus) and one species of reptiles (the Hermann tortoise Testudo hermanni) to widely assess three issues: 1) the use of environmental geometry with and without landmarks; 2) the role of two geometric tasks, one driven by spontaneous behaviour (“social-cued memory task”) and the other by learning processes (“rewarded exit task”); 3) the involvement of extra-visual sensory channels in visual transparency conditions, and motion patterns. The present Thesis applied behavioural assessments and analyses to pursue a line of comparison, across species, methodologies, and sensory systems. As regards environmental geometry and landmarks in fish and tortoises (Chapter 2), the studies were carried out within several apparatuses, that is, a rectangular opaque arena or two different sized square opaque arenas or a transparent square arena, with conspicuous or local landmarks: Study 1, Conspicuous landmark (blue wall) in zebrafish; Study 2: Local landmarks (corner panels) in zebrafish; Study 3, Environmental geometry in tortoises; Study 4, Conspicuous landmark (blue wall) in tortoises. As regards spontaneous vs. acquired geometric spatial reorientation in fishes (Chapter 3), the studies were carried out within a rectangular or square transparent arena, with or without geometric cues or a 3D landmark: Study 5, Nonvisual environmental geometry in zebrafish, redtail splitfin fish, and goldfish; Study 6, Isolated environmental geometric cues in zebrafish; Study 7, 3D outside landmark (blue cylinder) in zebrafish. As regards extra-visual sensory systems and motion patterns in fish (Chapter 4), one study was carried out within a rectangular transparent arena: Study 8, Lateral line pharmacological ablation in zebrafish. In respect of comparisons among species, overall results suggested that zebrafish, redtail splitfin fish, and goldfish reoriented similarly through transparent surfaces, which defined a distinctive global shape, supporting spatial reorientation under undefined situations (e.g., seek out food within a visually lacking and unenriched environment) as a shared skill among teleosts, despite ecological specificities. Likewise, the Hermann tortoise reoriented within a geometric environment with precision to meet a survival need, suggesting that even non-nomadic species that hibernate for long can benefit from orientation by extended terrain surfaces. In respect of memory tests (“working” vs. “reference”, spontaneous vs. acquired), overall results indicated that the rewarded exit task designed to train fish and tortoise to reorient required learning processes allowing them to overcome natural predispositions to improve other related abilities, such as landmark-use. The dissociation between working and reference memory in spatial domain must be considered highly dependent on task’s demands where attentional factors determine short-term memories and motivational states long-term ones. In respect of sensory channels and motion patterns, overall results revealed that fish and tortoises used modalities driven by touch, in synch with sight, to determine geometric parameters during spatial reorientation. Therefore, a promising link between other vertebrates and humans takes place, in consideration of orientation mechanisms used to face situations of visual deprivation or impairments. The present Thesis may even contribute to a general understanding of reorientation behaviour in phylogenetically remote vertebrate species, thus supporting the widespread use of geometry-grounded tools in everyday activities. This also provides comparative support among species that inhabit on Earth and share cognitive adaptations to deal with similar requests.