This talk will review a number of emerging research topics which we have been studying in the area of sensing, imaging, and inverse problems. In particularly, we will discuss progress on two problems: dynamic acquisition of data based on Bayesian posterior models, and effective methods for prior modeling of data using advance denoising models. We also look at the problem of image modeling in a broader contact, and make a variety of observations about aspects of image modeling that can be improved, and better ways of integrating forward and prior models using plug and play prior methods.