Catalytic hydrogenation of a biomass-derived molecule, levulinic acid (LA), to γ-valerolactone (GVL) has been getting much attention from researchers across the globe recently. This is because GVL has been identified as one of the potential molecules for replacing fossil fuels. For instance, GVL can be catalytically converted into liquid alkenes in the molecular weight range close to that found in transportation fuels via a process that does not require an external hydrogen source. Noble and non-noble metals have been used as catalysts for the selective hydrogenation of LA to GVL. Of these, Ru has been reported to be the most active metal for this reaction. The type of metal supports and solvents has been proved to affect the activity, selectivity, and yields of GVL. Water has been identified as a potential, effective “green” solvent for the hydrogenation of LA to GVL. The use of different sources of H2 other than molecular hydrogen (such as formic acid) has also been explored. In a few instances, the product, GVL, is hydrogenated further to other useful products such as 1,4-pentanediol (PD) and methyl tetrahydrofuran (MTHF). This review selectively focuses on the potential of immobilized Ru catalysts as a potential superior catalyst for selective hydrogenation of LA to GVL.