We discuss five topics related to inference and modeling in physics: image registration, magnetic image deconvolution, effective models of spin glasses, the two-dimensional Ising model, and a benchmark dataset of the arXiv pre-print service. First, we solve outstanding problems with image registration (which aims to infer the rigid shift relating two or more noisy shifted images), obtaining the information-theoretic limit in the precision of image shift estimation. Then, we use Bayesian inference and develop new physically-motivated priors in order to solve the ill-posed deconvolution problem of reconstructing electric currents from a magnetic images. After that, we apply machine learning and information geometry to study a spin glass model, finding that this model of canonical complexity is sloppy and thus allows for lower-dimensional effective descriptions. Next, we address outstanding questions regarding the corrections to scaling of the two dimensional Ising model by applying Normal Form Theory of dynamical systems to the Renormalization Group (RG) flows and raise important questions about the RG in various statistical ensembles. Finally, we develop tools and practices to cast the entire arXiv pre-print service into a benchmark dataset for studying models on graphs with multi-modal features.