I will discuss ε-independence, which is an interpolation of classical and free independence originally studied by Motkowski and later by Speicher and Wysoczanski. To be ε-independent, a family of algebras in particular must satisfy pairwise classical or free independence relations prescribed by a {0,1}-matrix ε, as well as more complicated higher order relations. I will discuss how matrix models for this independence may be constructed in a suitably-chosen tensor product of matrix algebras. This is joint work with Benoit Collins.