  We prove that distribution dependent (also called McKean--Vlasov) stochastic
delay equations of the form \begin{equation*} \mathrm{d}X(t)=
b(t,X_t,\mathcal{L}_{X_t})\mathrm{d}t+
\sigma(t,X_t,\mathcal{L}_{X_t})\mathrm{d}W(t) \end{equation*} have unique
(strong) solutions in finite as well as infinite dimensional state spaces if
the coefficients fulfill certain monotonicity assumptions.
