Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, A>, A>), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, A> is the opposite of , while A> is the neutral (or indeterminate) between them, i.e., neither nor A>. See http://fs.gallup.unm.edu/neutrosophy.htm. Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x), that satisfy some axioms, for each element x in a given set. This Special Issue gathers original research papers that report on state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016, but have gained interest from world researchers, and several papers have been published in first rank international journals.