The intersection set of Bayesian and nonparametric statistics was almost empty until about 1973, but now seems to be growing at a healthy rate. This chapter gives an overview of various theoretical and applied research themes inside this field, partly complementing and extending recent reviews of Dey, Müller and Sinha (1998) and Walker, Damien, Laud and Smith (1999). The intention is not to be complete or exhaustive, but rather to touch on research areas of interest, partly by example.