This minicourse focuses on counting and equidistribution in homogeneous spaces. We will discuss results for rank-one settings in detail, while briefly surveying developments in the higher-rank case. The first lecture explains how to derive Haar mixing from Bowen-Margulis-Sullivan mixing by analyzing transversal intersections, a technique developed by Roblin. The second lecture applies these mixing results to study the distribution of Jordan and Cartan spectra, which correspond to counting closed geodesics and orbit points, respectively.