The quantitative analysis of probabilistic programs answers queries involving the expected values of program variables and expressions involving them, as well as bounds on the probabilities of assertions. In this chapter, we will present the use of concentration of measure inequalities to reason about such bounds. First, we will briefly present and motivate standard concentration of measure inequalities. Next, we survey approaches to reason about quantitative properties using concentration of measure inequalities, illustrating these on numerous motivating examples. Finally, we discuss currently open challenges in this area for future work.