  Bayesian nonparametric space partition (BNSP) models provide a variety of
strategies for partitioning a $D$-dimensional space into a set of blocks. In
this way, the data points lie in the same block would share certain kinds of
homogeneity. BNSP models can be applied to various areas, such as
regression/classification trees, random feature construction, relational
modeling, etc. In this survey, we investigate the current progress of BNSP
research through the following three perspectives: models, which review various
strategies for generating the partitions in the space and discuss their
theoretical foundation `self-consistency'; applications, which cover the
current mainstream usages of BNSP models and their potential future practises;
and challenges, which identify the current unsolved problems and valuable
future research topics. As there are no comprehensive reviews of BNSP
literature before, we hope that this survey can induce further exploration and
exploitation on this topic.
