This thesis looks into the holonomy algebras of Tractor/Cartan connections for both projective and conformal structures. Using a splitting formula and a cone construction in the Einstein case, it classifies all reductive, non-irreducible holonomy groups for conformal structures (thus fully solving the question in the definite signature case). The thesis then analyses the geometric consequences of of holonomy reduction for the projective Tractor connection. A general, Ricci-flat, cone construction pertains in the projective case, and this thesis fully classifies the irreducibly acting holonomy algebras by analysing which holonomy families admit a torsion-free Ricci-flat affine connection, and constructing cones with these properties.