Interacting particle systems (IPS) play an important role in many applied sciences, both as a modelling framework for social and biological phenomena and as a tool for statistical algorithms used in data science and uncertainty quantification.  These two aspects are often intertwined as, for example, certain algorithms are inspired by dynamics observed in nature. While the use of IPS is now classical in fields such as filtering, recent exciting developments at the interface with PDE and optimal transport theory on the one hand and data science and uncertainty quantification on the other, have initiated fast progress in the design and analysis of new algorithms. In this talk I will discuss how tools from PDE theory and optimal transport can be used to analyse and guide the behavior of IPS based algorithms.  One particular example of interest will be the performance of IPS based methods for inverse problems with expensive and noisy likelihoods.