Vertex algebras are a notoriously hard topic to introduce. Their axioms are complicated and the formalism (which comes from CFTs) is written in terms of objects, like quantum fields, that can feel unfamiliar to the average mathematician. The aim of this talk is to give a gentle introduction to vertex algebras and related structures using a different formalism, centred around the $\lambda$-bracket. This is a structure conceptually similar to a Lie bracket, which helps giving the topic a more familiar, algebraic feeling.