2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138653We describe various approaches to understanding Fukaya categories of cotangent bundles. All of the approaches rely on introducing a suitable class of noncompact Lagrangian submanifolds. We review the work of Nadler-Zaslow (math/0604379, math/0612399) and the authors (math/0701783), before discussing a new approach using family Floer cohomology and the ``wrapped Fukaya category''. The latter, inspired by Viterbo's symplectic homology, emphasises the connection to loop spaces, hence seems particularly suitable when trying to extend the existing theory beyond the simply-connected case.27 pages, 2 figures. Version 4 -- application added (to exact Lagrangians in Euclidean space which are standard at infinity), results sharpened for cotangent bundles of toriSymplectic GeometryAlgebraic Topology53D35; 53D40; 57T30text