Bayesian statistics has enjoyed a marked resurgence in research, computation and application over the past 50 years, and has permeated almost every domain of scientific investigation over the past decade. These approaches are attractive in the so-called 'big data era', particularly due to their ability to model and analyse complex systems, manage and merge diverse data sources, provide probabilistic inferences under uncertainty and iteratively update or learn as new information arrives. However, challenges remain when applying these methods to substantive 'real-world' problems. In this presentation, I will discuss some of our experiences in developing Bayesian models, priors and computational solutions for a range of such problems in health and environmental domains. This work is joint with a number of co-authors, listed below.