In this talk we discuss the existence and the importance of asymptotic colengths for families of \(m\)-primary ideals in a Noetherian local ring \((R,m)\).  We explore various families such as weakly graded families, weakly \(p\)-families and weakly inverse \(p\)-families and discuss a new analytic method to prove the existence of limits. Additionally, if time permits we will talk about Minkowski type inequalities, positivity results, and volume = multiplicity formulas for these families of ideals. This talk is based on a joint work with Cheng Meng.