One example is the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) algorithm, that takes advantage of the sparsity of the wave functions, and deadwoods are not (or rarely) processsed and stored along the FCIQMC optimization procedure. FCIQMC is a projective method that stochastically propagates the imaginary-time Schrödinger's equation to solve the CI-problem. Apart from being a sparse CI-eigensolver it can be near-linearly parallelized to benefit from modern hardware. The use of FCIQMC as the CASSCF CIeigensolver within the Super-CI framework, termed Stochastic-CASSCF, was developed in our group and has been applied with great success to circumvent the active space size limits of conventional CASSCF. Examples of methodologies where truncated CI spaces are pre-selected include the generalized valence bond approach, constrained-CASSCF (CCASSCF), quasi-CASSCF (QCASSCF), restricted-CI (RCI), restricted active space self-consistent field (RASSCF), the occupation restricted multiple active spaces self-consistent field (ORMAS-SCF) method, and the generalized active space self-consistent field (GASSCF) approach. In CCASSCF the active space is partitioned into several subspaces with a fixed number of particles per subspace; the method is formulated in a basis of CSFs. QCASSCF works like CCASSCF but is formulated in a basis of Slater determinants. RAS wave functions are defined using three active subspaces, commonly labelled RAS1, RAS2, and RAS3, with RAS1 containing doubly occupied orbitals, RAS3 containing empty orbitals, and RAS2 containg orbitals with occupation numbers ranging from 0 to 2. The maximum number of holes in RAS1 and the maximum number of particles in RAS3 are used as restrictions to define the configuration interaction space. In the ORMAS-SCF method, implemented in the GAMESS-US chemistry software package, several active spaces are chosen; all intra-space excitations are allowed while the number of interspace excitations are restricted by local minimum and maximum occupation numbers per active subspace. The corresponding CI problem is solved in the Slater determinant basis, relying on the Slater-Condon rules. The similar concept of generalized active space (GAS) was introduced by Jeppe Olsen already in 1988. In 2011, the GAS approach was coupled to the Super-CI algorithm within the (Open)Molcas chemistry software package for the variational orbital relaxation, leading to GASSCF. As in OR-MAS, the truncated GAS wave functions are built by selecting a number of active subspaces, and imposing constraints at the level of the interspace excitations. However, GASSCF differs from ORMAS-SCF in a number of aspects; most notably, in GAS interspace excitation constraints are enforced via cumulative minimum and maximum occupation numbers, instead of the local constraints of the ORMAS scheme, and a spin-adapted basis of CSFs is used in the GAS method, relying on the Graphical Unitary Group Approach (GUGA). GAS-like truncated CI wave functions have also been implemented in the Molpro package. GAS restrictions can be used to exclude deadwood configurations and to reduce the computational costs while retaining highly accurate multi-reference predictions. This strategy has been adopted in the 2011 work and applied to the dissociation curve of the Gd 2 dimer and to the study of the relative stability of two energetically low-lying spin states of the Oxo-Mn(salen) complex. The GAS strategy can also be applied to investigate the role of specific electron correlation mechanisms, by removing electronic confifurations that are relevant to describe those correlation pathways. This strategy was undertaken in our group to quantify the effect of the correlation enhanced π-backdonation in Fe(II)-porphyrins, and to understand correlation effects in corner-sharing cuprates. Selected-CI methods are another class of MC techniques that attempt to circumvent the exponential scaling limitation by selecting the important electronic configurations on the fly using automated heuristics. These methodologies heavily rely on the Slater-Condon rules and are generally bound to a Slater determinant many-body basis. Another notable strategy that reduces the exponential scaling limitation is the Density Matrix Renormalization Group (DMRG) theory. In this work we introduce a flexible Stochastic-GAS method, that stochastically optimizes truncated GAS wave functions expanded in the Slater determinant many-body basis, based on the FCIQMC algorithm. In one of our earlier works, we introduced a prototype Stochastic-GAS implementation that supported only disconnected GAS subspaces, in that similar to the QCAS strategy, and successfully applied it to an Fe(II)-porphyrin model system, to probe the effect of the correlation enhanced σ-donation/π-backdonations on the basis of a large CAS (32, 34) active space. The GAS algorithm here described also supports interspace excitations that can be restricted by both cumulative and local minimum and maximum occupation numbers constraints, as in the conventional GASSCF method, and in ORMAS-SCF, respectively.