Automorphism groups of right-angled Artin groups (RAAGs) lie at the intersection of geometric group theory and algebraic topology and have been studied a lot. In this talk, we focus on computing the virtual cohomological dimension (vcd) of outer automorphism groups of RAAGs. I will present an algorithm recently developed by Day and Wade that enables such computations. The algorithm breaks the outer automorphism group down using short exact sequences and can be visualized as a tree-like structure, reflecting the recursive decomposition process. It is quite intricate, and I will illustrate the method using concrete examples.