  We develop a discrete framework for the interpolation of Banach spaces, which
contains the well-known real and complex interpolation methods, but also more
recent methods like the Rademacher, $\gamma$- and $\ell^q$-interpolation
methods. Our framework is based on a sequential structure imposed on a Banach
space, which allows us to deduce properties of interpolation methods from
properties of sequential structures. Our framework has a formulation modelled
after both the real and the complex interpolation methods. This enables us to
extend various results, previously known only for either the real or the
complex interpolation method, to all interpolation methods that fit into our
framework. As applications, we prove an interpolation result for analytic
operator families and an interpolation result for intersections.
