Catalytic CO2 conversion to clean fuels and chemicals using hydrogen produced from water with renewable energy is important for mitigating the climate change and reducing the dependence on fossil energy resources. This review summarizes recent advances in CO2 hydrogenation to alcohols and hydrocarbons via heterogeneous catalysis based on the publications in the past decade focusing on metal-based catalysts and also including oxide- and zeolite-based catalysts. Generally, adsorption and activation are more difficult for CO2 than for CO in catalytic hydrogenation over metal catalysts. CO2 conversion to alcohols and hydrocarbons are two major routes that have been explored the most, and the path to a given type of products depends on whether the first hydrogen atom is added to carbon or oxygen of CO2 on surface and the subsequent transformation under the given reaction conditions. Significant advances have been made in both experimental and computational studies on metal-based catalysts. Effective catalysts and processes are required to minimize CO and CH4 and to selectively foster CO2 conversion to alcohols at lower temperatures, particularly to higher alcohols with much less thermodynamic restraint. While Cu-based catalysts have been widely studied, some new bimetallic catalysts such as Pd-Cu and Pd-Zn and oxide-based catalysts such as In2O3 offer promise with higher selectivity toward methanol. Rh-based bimetallic catalysts show selectivity to ethanol and higher alcohols. While new catalysts for CO2 methanation such as Co/ZrO2 has been developed, more progress has been achieved in developing catalysts for synthesis of C2 + higher hydrocarbons from CO2 in a single stage, which is in sharp contrast to the previous approach to hydrogenate CO2 to CO in the first stage followed by conversion of CO in the second stage. New bimetallic catalysts and mixed oxides have been found to be effective for more selective synthesis of C2-C4 olefins, C5 + liquid hydrocarbons and aromatics. Significant progress has been achieved in synthesizing C2 + and C5 + higher hydrocarbons with very little CH4 in one-stage using hybrid catalysts such as In2O3 or Fe3O4 plus ZSM-5 type zeolite. This review highlights the progress in clarifying the key factors such as types of metals, supports and catalyst formulations affecting the activity and selectivity of CO2 conversion, and in understanding of reaction pathways as well as catalyst composition-structure-activity relationship. The field of CO2 hydrogenation still requires significant advance in developing fundamental understanding of catalytically active phase, active sites and reaction mechanisms for CO2 activation and C-C coupling for synthesis of higher alcohols and higher hydrocarbons, as well as efforts in innovative catalytic processes for energy-efficient CO2 conversion and utilization.