Nonparametrics plays an important role in Bayesian modelling: nonparametric models are flexible, realistic and by providing good coverage can guard against model inadequacy. Modern Bayesian nonparametrics builds on decades of research on Dirichlet and Gaussian processes to develop new models for complex data sources. I will briefly cover some examples of our recent work in this area: models for overlapping clustering and sparse arrays, probabilistic models of social and biological networks, diffusion tree models for hierarchical clustering, and models for covariance and volatility based on copulas and generalised Wishart processes. I will end on some discussion of limitations, links to classical nonparametrics, and directions for theory.