We report on a database, named BIL&GIN, designed for investigating the cognitive, behavioral, genetic, and brain morphological/functional correlates of hemispheric specialization. The database contains records from a sample of 453 adult participants enriched in left-handers (45%, N=205) as compared to the general population. For each subject, socio-demographic data, hand and eye laterality, family handedness, and cognitive abilities in the language, motor, visuo-spatial, and numerical domains have been recorded. T1-MRI and DTI data were also acquired, as well as resting-state functional MRI. Task-evoked functional MRI was performed in a sub-sample of 303 subjects (157 left-handers) using a customized functional battery of 16 cognitive tasks exploring the same three cognitive domains. Performances at the tasks executed in the magnet as well as post-acquisition debriefing were recorded. A saliva sample was obtained from the subjects of this sub-sample from which DNA was extracted. The BIL&GIN contains results of imaging data processing for each subject, namely maps of tissue (GM, WM, CSF) probability, cortical thickness, cortical surface, and diffusion parameters as well as regional values of these phenotypes for regions of both AAL and FreeSurfer parcellations. For the subjects who underwent FMRI, individual SPM contrast maps for each of the 8 runs were also calculated and included in the database, as well as corresponding BOLD variations in ROIs of the AAL and AICHA atlases, and Wilke's hemispheric functional lateralization index. The BIL&GIN data sharing is based on a collaborative model.