 Compositionality has always been an important concern in the use of logical systems in natural language semantics (see the entry on  compositionality).  Through the use of higher order logics (see the entries on  second-order and higher-order logics  and  Church’s type theory),  a thoroughly compositional account of, e.g., the quantificational system of natural language can be achieved, as is demonstrated in classical Montague grammar (Montague 1974a,b, 1973; compare the entry on  logical form).  We will review how the dynamic approach can be extended to higher order systems. The link between dynamic semantics and type theory is more like a liaison than a stable marriage: there is no intrinsic need for the connection. The connection is treated here to explain the historical influence of Montague grammar on dynamic semantics.