Blobbed topological recursion

We describe the formalism and the properties of the blobbed topological recursion, which provides the general solution of a set of abstract loop equations. This procedure extends the topological recursion by introducing extra terms (blobs) in the initial conditions for each multidifferential $\omega_{g,n}$. We apply this formalism to topological expansion of formal Hermitian matrix models (the blobs are necessary to include arbitrary interactionsm) and pose some open questions.