I will explain the construction of the Fukaya-Morse category of a Riemannian manifold X -- an A-infinity category (a category where associativity of composition holds only "up- to-homotopy") where the higher composition maps are given in terms of numbers of embedded trees in X, with edges following the gradient trajectories of certain Morse functions. I will give simple examples and explain different approaches to understanding the structure and proving the quadratic relations on the structure maps -- (1a) via homotopy transfer, (1b) effective field theory approach, (2) topological quantum mechanics approach. The talk is based on a joint work with O. Chekeres, A. Losev and D. Youmans, arXiv:2112.12756.