In this talk, we will focus on uninorms and n-uninorms with continuous underlying functions. We will discuss the ordinal sum construction for uninorms, their characterizing set-valued functions and decomposition of uninorms with continuous underlying functions into semigroups related to continuous Archimedean t-norms and t-conorms, representable uninorms and idempotent semigroups. Similarly, we will discuss characterizing set-valued functions of n-uninorms and decomposition of n-uninorms with continuous underlying functions into z-ordinal sum of idempotent and generated semigroups.