Explore the intricacies of flatbands in translationally invariant systems through this 30-minute conference talk by Alexei Andreanov from PCS Institute for Basic Science. Delve into the construction and perturbation of flatbands, understanding their dispersionless nature and the presence of compact localized states. Examine the extreme sensitivity of flatbands to perturbations and their potential as hosts for unconventional phases of matter. Learn about recent progress in constructing flatbands in various settings, including in the presence of a d.c. field. Discover how systematic construction allows for a better understanding of flatband response to perturbations such as disorder and interactions, leading to the emergence of nonergodic phases. Follow the comprehensive outline covering technical definitions, construction methods, classification, real and Bloch space constructions, perturbations, and future directions in flatband research.