  Over the past 50 years, Nelson algebras have been extensively studied by
distinguished scholars as the algebraic counterpart of Nelson's constructive
logic with strong negation. Despite these studies, a comprehensive survey of
the topic is currently lacking, and the theory of Nelson algebras remains
largely unknown to most logicians. This paper aims to fill this gap by
focussing on the essential developments in the field over the past two decades.
Additionally, we explore generalisations of Nelson algebras, such as
N4-lattices which correspond to the paraconsistent version of Nelson's logic,
as well as their applications to other areas of interest to logicians, such as
duality and rough set theory. A general representation theorem states that each
Nelson algebra is isomorphic to a subalgebra of a rough set-based Nelson
algebra induced by a quasiorder. Furthermore, a formula is a theorem of Nelson
logic if and only if it is valid in every finite Nelson algebra induced by a
quasiorder.
