Susceptibilities and optical conductivity are examples of two-particle response functions that are the key quantities for connecting theoretical predictions for corelated materials with experimental results. It can however become highly nontrivial to calculate them, especially in cases when nonlocal electronic correlations are important. In my talk I will explain what two-particle correlations are and when they become important. I will then present an overview of methods of their computation with the focus on diagrammatic methods. I will show results for two-particle (vertex) corrections to optical conductivity], that are present in systems with antiferromagnetic or charge density wave fluctuations, leading to a displaced Drude peak in correlated metals. At the end I will discuss computational challenges and new methodological developments in the efficient representation of two-particle correlation functions with the use of quantics tensor trains.