Bayesian nonparametrics (BNP) studies Bayesian inference on nonparametric models, where the parameter of interest is infinite-dimensional. For example, we study posterior distributions of regression functions and densities. Applications of BNP are numerous, ranging from image analysis, neural networks, machine learning to climate modelling, genetics and speech recognition. My research involves understanding the issue of putting priors on infinitedimensional spaces, and developing Bayesian methodologies and computation strategies for nonparametric problems. In this talk, I will discuss two aspects of my current research. First, I will talk about Bayesian sequential procedures that “actively” learn from past experience. I propose a new way of thinking about Bayesian estimation that combines the use of posteriors and credible sets through a two-stage approach. In my procedure, second stage samples are obtained from a suitable credible set constructed based on first stage posterior distribution. Second, I will discuss wavelet spike-and-slab priors and a Bayesian Lepskiâ€^TMs method to estimate regression functions, and will further touch upon issues such as lower limit on adaptation and priors for discrete wavelet transform. I will end by discussing some ongoing and future projects