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 interactions) and pose some open questions.