The Second Random Phase Approximation (SRPA) is a natural extension of RPA where more general excitation operators are introduced. These operators contain, in addition to the one particle-one hole configurations already considered in RPA, also two particle-two hole excitations. Only in the last years, large-scale SRPA calculations have been performed, showing the merits and limits of this approach. In the first part of this paper, we present an overview of recent applications of the SRPA based on the Skyrme and Gogny interactions. Giant resonances in 16O will be studied and their properties discussed by using different models. In particular, we will present the first applications of the SRPA model with the finite-range Gogny interaction, discussing the advantages and drawbacks of using such an interaction in this type of calculations. After that, some more recent results, obtained by using a subtraction procedure to overcome double-counting in the SRPA, will be discussed. We will show that this procedure leads to results that are weakly cutoff dependent and that a strong reduction of the SRPA downwards shift with respect to the RPA spectra is found. Moreover, applying this procedure for the first time in the Gogny-SRPA framework, we will show that this method is able to reduce the anomalous shift found in previous calculations and related to some proton-neutron matrix elements of the residual interaction.