Weitzman's price-quantity analysis framework has been widely used, and in the field of climate economy it is applied to choose proper emissions reduction instruments for best welfare under uncertainty. This article summarizes the principle and method of selecting carbon emission reduction instruments by price versus quantities decision criterion. The probability of uncontrollable outcomes under uncertainty is reduced by comparing marginal abatement costs with marginal abatement benefits. On this basis, the following outreach research are summarized on some key issues such as dynamic analysis, assumptions improvements, elements expansion and hybrid policies. This topic drives a lot of research but no review has been conducted. We sum up the time-correlated cost and multi-period policy research to extend the static framework to dynamic analysis. There are also many studies that relax the strong assumptions of original framework including correlated uncertainty between cost and benefit, stock effect of carbon, nonlinear marginal cost and benefit, distributional inefficiency and extension of partial equilibrium. In addition, more elements around emissions control have been included and specified such as uncertainty, incomplete enforcement, technology innovation and multiple pollutants. We also summarize the researches of hybrid policy which combines quantity and price control to be a new regulation method and dual regulation which suggest applying both quantity and price control in different departments. It is found that early researches favor carbon tax while quantity regulation has gradually become popular. Finally, this article puts forward some research directions worth more exploring at both theory and application level.