I will describe how the orbit method can be developed in a quantitative form, along the lines of microlocal analysis, and applied to local problems in representation theory and global problems involving the analysis of automorphic forms. This talk will overlap with a number theory seminar given last semester, but will be aimed instead towards people who are not necessarily number theorists, and could be considered as a retroactive introduction to that seminar. The results and methods to be surveyed are the subject of the following papers/preprints:   https://arxiv.org/abs/1805.07750   https://arxiv.org/abs/2012.02187   https://arxiv.org/abs/2109.15230