Lignin holds tremendous and versatile possibilities to produce value-added chemicals and high performing polymeric materials. Over the years, different cutting-edge lignin depolymerization methodologies have been developed, mainly focusing on achieving excellent yields of mono-phenolic products, some even approaching the theoretical maximum. However, due to lignin's inherent heterogeneity and recalcitrance, its depolymerization leads to relatively complex product streams, also containing dimers, and higher molecular weight fragments in substantial quantities. The subsequent chemo-catalytic valorization of these higher molecular weight streams, containing difficult-to-break, mainly C-C covalent bonds, is tremendously challenging, and has consequently received much less attention. In this minireview, we present an overview of recent advances on the development of sustainable biorefinery strategies aimed at the production of well-defined chemicals and polymeric materials, the prime focus being on depolymerized lignin oils, containing high molecular weight fractions. The key central unit operation to achieve this is (bio)catalytic funneling, which holds great potential to overcome separation and purification challenges.