The need for optimal control of processes under a restricted amount of resources renders first order optimization methods a viable option. Although computationally cheap, these methods typically suffer from slow convergence rates. In this work we discuss the family of first order methods known as decomposition schemes. We present three popular methods from this family, draw the connections between them and report all existing results that enable acceleration in terms of the convergence rate. The approach for splitting a problem into simpler ones so that the accelerated variants can be applied is also discussed and demonstrated via an example.