The fundamental cause of global warming is carbon emission. The traditional mode of economic development is highcarbon economy. In contrast, lowcarbon economy features the reduction of carbon dioxide (CO2) and other greenhouse gases (GHG). Carbon dioxide emission and emission reduction are classical environmental issues resulting from cross-border externalities and intergenerational externalities, which lead to the ″Giddens Paradox″. Cutting down on carbon dioxide emission is a crucial step in the development of a low carbon economy. In practice, there are two major policies that have been widely applied in developed countries to control the pollutants. One is the fiscal and tax policy based on the theory of Pigou-tax; another follows Cap-and-Trade which originated from Coase Theorem. The hypothesis of ″Double Dividend″ is attractive to researchers and policy-makers, but should be subjected to more careful empirical analysis and the Cap-and-Trade mechanism design in China and worldwide needs improvement. Future research on low carbon economy may focus on the initial distribution of carbon dioxide permits, selection of carbon reduction policies, cost-benefit analysis of carbon reduction, policy design of regional carbon reduction, as well as the relevance between carbon reduction and energy pricing mechanism.