The Bayesian paradigm provides a natural framework for the theory and practice of statistics. In this presentation, I will consider the various components of Bayesian models, including priors and likelihoods, and some aspects of Bayesian computation, including MCMC and ABC, in the context of some challenging problems that we have been tackling. These problems include monitoring the health of the Great Barrier Reef, developing an online, interactive atlas of cancer for Australia, and reducing congestion at airports. My collaborators on these projects are members of our Bayesian Research and Applications (BRAG) group at QUT and the Australian Research Council Centre of Excellence in Mathematical and Statistical Frontiers (ACEMS).