  This paper presents a systematic study of coproducts. This is carried out
principally, but not exclusively, for finitely generated quasivarieties A that
admit a (term) reduct in the variety D of bounded distributive lattices. In
this setting we present necessary and sufficient conditions on A for the
forgetful functor U from A to D to preserve coproducts. We also investigate the
possible behaviours of U as regards coproducts in A under weaker assumptions.
Depending on the properties exhibited by the functor, different procedures are
then available for describing these coproducts. We classify a selection of
well-known varieties within our scheme, thereby unifying earlier results and
obtaining some new ones. The paper's methodology draws heavily on duality
theory. We use Priestley duality as a tool and our descriptions of coproducts
are given in terms of this duality. We also exploit natural duality theory,
specifically multisorted piggyback dualities, in our analysis of the behaviour
of the forgetful functor into D. In the opposite direction, we reveal that the
type of natural duality that the class A can possess is governed by properties
of coproducts in A and the way in which the classes A and U(A) nteract.
