This comprehensive review elucidates recent numerical and empirical investigations of laminar-scale, free convection heat transport within two and three-dimensional enclosures filled with nanofluids and hybrid nanofluids. A particular emphasis is placed on previously explored enclosure geometries, ranging from simplistic to complex regular shapes. It is identified that a research gap exists within three-dimensional numerical investigations of both simple and complex enclosures. The study reveals that the local peak of the Nusselt number on the surfaces of the cylinder and the enclosure manifests at the locations where the shortest distance is observed between the cylinder surface and the enclosure wall. At lower Rayleigh numbers (Ra), the heat transfer demonstrates a decreasing trend with increasing values of volume fraction for oxide nanofluids. Upon increasing Ra, total heat generation is noted to decrease for all volume fractions and all positions of the conductive baffle. The Bejan and average Nusselt numbers display an inverted relationship to each other for the same range of Rayleigh numbers and solid volume fractions. Interestingly, the average Bejan numbers augment and the entropy generations remain approximately constant at high Rayleigh numbers. The analysis further unveils that the heat transfer rate experiences an increase with higher values of solid volume fraction and Rayleigh numbers. The average Nusselt number shows an increasing trend with the rise of the Hartmann number. Additionally, the heat transfer rate witnesses an enhancement with the increased concentration of Carbon Nanotube (CNT) particles and Rayleigh numbers. This review underscores the need for future research to address the present gaps and to further our understanding of heat transfer dynamics in nanofluid-filled enclosures.