By relying on the theory presented in Chap. 7 , this chapter focuses on two-stage stochastic optimization problems and two-stage decomposition to formulate a non-smooth optimization model so that the cutting-plane and bundle method algorithms from Chaps. 10 , 11 , and 13 can be efficiently deployed. The chapter extensively discusses how to set up appropriate black boxes (oracles) to satisfy the required conditions by those algorithms. A particular emphasis is given to inexact oracles of lower and upper types that permit solving general two-stage stochastic optimization models efficiently.