Vertex operator algebra (VOA) is the algebraic setup formalising conformal field theory. It develops in a mathematically complete way the idea of constructing quantum field theory using the algebra of symmetry currents and their modules. On the other hand, conformal loop ensembles (CLE) are measures on random loop configurations that are known, in certain cases, to describe the continuous limit of statistical models at critical points. There is a one-parameter family of such measures, supposed to correspond to all central charges between 0 and 1. These two constructions enjoy complete mathematical rigour, and give the opportunity to understand with more precision the relation between the statistical interpretation of QFT, and its algebraic description. I will describe some of my recent works in this direction: I will explain how to construct the Virasoro VOA (the stress-energy tensor and its descendents) in terms of random objects in CLE. No prior knowledge of either VOA or CLE is needed as I will review both subjects.