  A collision model (CM) is a framework to describe open quantum dynamics. In
its {\it memoryless} version, it models the reservoir $\mathcal R$ as
consisting of a large collection of elementary ancillas: the dynamics of the
open system $\mathcal{S}$ results from successive "collisions" of $\mathcal{S}$
with the ancillas of $\mathcal R$. Here, we present a general formulation of
memoryless {\it composite} CMs, where $\mathcal S$ is partitioned into the very
open system under study $S$ coupled to one or more auxiliary systems $\{S_i\}$.
Their composite dynamics occurs through internal $S$-$\{S_i\}$ collisions
interspersed with external ones involving $\{S_i\}$ and the reservoir $\mathcal
R$. We show that important known instances of quantum {\it non-Markovian}
dynamics of $S$ -- such as the emission of an atom into a reservoir featuring a
Lorentzian, or multi-Lorentzian, spectral density or a qubit subject to random
telegraph noise -- can be mapped on to such {\it memoryless} composite CMs.
