Multivector fields are a natural generalization of Forman’s combinatorial vector fields. They provide greater flexibility in the description of a variety of dynamical phenomena, and they can be used to combinatorialize even such concepts as chaotic behavior or multiflows. In the present chapter, we review basic notions from combinatorial multivector fields on Lefschetz complexes and show that they provide a natural framework for our theory of connection matrices. This is achieved through a straightforward construction of an associated acyclic partition of the underlying Lefschetz complex.