Bayesian methods offer an attractive general approach for modelling complex data, due to their internal consistency and appealing statistical properties. However, traditional approaches assume that the order in which observations are collected does not matter, an assumption that is violated in a variety of modern applications. To overcome this limitation, we will investigate approaches able to account for more general types of dependence among observations. In particular, we will investigate methodological and computational issues related to dependent priors within the Bayesian framework. Emphasis will be given to the development of suitable priors for functional data analysis and temporal modelling.