Beyond hexagons, a distinctive family of pentagonal two-dimensional materials (2DMs) has emerged, featuring asymmetric geometry, exotic characteristics, and promising applications. Pentagonal tessellation of 2DMs generally leads to semiconducting bandgaps and directional electrical and optical properties. The theoretical prediction of penta-graphene and the experimental realization of materials, such as PdSe2, PdPSe, PdPS, and NiN2, have revealed a new horizon for penta-materials, showcasing high air stability and inherent auxeticity. Due to the rarity of pentagonal topology in nature, it is crucial to employ computational models and simulations to establish the stable configurations of these materials and understand their behavior in pentagonal arrangements. Consequently, the multitude of theoretically predicted penta-materials far surpasses the number of experimentally synthesized ones, numbering in the hundreds. A comprehensive catalog encapsulates recent progress, properties, and future perspectives, unlocking their full potential and paving the way for experimental realization. This review presents an extensive compilation of predicted penta-materials to date, elucidating their properties and potential applications.