Second Random Phase Approximation (SRPA) is a natural extension of RPA obtained by introducing more general excitation operators where 2 particle-2 hole configurations, in addition to the 1 particle-1 hole ones, are considered. First, some formal properties of SRPA are presented and the issue of the of the rearrangement terms to be used in the matrix elements beyond the standard RPA ones is discussed. Current versions of SRPA are usually based on non-interacting 2 particle-2 hole configurations, i.e. only the interaction between 2 particle-2 hole and 1 particle-1 hole configurations is taken into account, in the so-called "diagonal" approximation. Some SRPA results with a Skyrme force in $^{16}$O are presented. The coupling between 1 particle-1 hole and 2 particle-2 hole as well as that between 2 particle-2 hole configurations among themselves are fully taken into account. Different levels of approximation will be then compared. Two approximations are employed for the treatment of the rearrangement terms, neglecting them or evaluating them with the RPA prescription. Finally, the effect of the diagonal approximation is analyzed.