Since the early 80s a glorious friendship has existed between rational homotopy theory and commutative algebra (becoming increasingly dormant...). A deep analogy exists between these two fields, centring on the so-called homotopy Lie algebra of a topological space or local ring. Results and ideas have been passed back and forth across this bridge. I will start from basics and try to give an idea of what's going on on either side. Hopefully I will get to the beautiful dichotomy theorem, proven by Felix and Halperin on the topological side and Avramov on the algebraic side.