The worldwide climate issues such as the global warming and the sea level rising are becoming serious.In order to relieve the stress of environment,a lot of attempts have been made to reduce the emission of CO_2,which is the main component of greenhouse gases.CO_2 capture and conversion(C3)is an emerging technology,which directly converts the captured CO_2 into high value-added compounds or fuels such as formic acid,methanol and methane.Porphyrin metal-organic frameworks(PMOFs)are based on porphyrin or metalloporphyrin ligands and metal nodes.The combination of excellent thermal/chemical stability,strong absorption of visible light and long lifetime of excited state,and high CO_2 capture capacity paves the way for the applications of PMOFs in C3.In this review,we have firstly introduced the synthesis strategies of PMOFs,which are guided by framework topology,pillar-layer and metal-organic cage(MOC).With the good control of the pore sizes and thermal/chemical stability,the catalytic performances of PMOFs can be easily tuned:PMOFs that are prepared via the pillar-layer and MOC strategies are of relatively lower stability,and the ones that are guided by framework topology are of higher stability.Next,we have classified the types of PMOFs according to the secondary building units(SBUs).There are four types of PMOFs,and the SBUs include(1)the low-valence metal ions such as Cu~(2+) and Cd~(2+);(2)the paddle-wheel M_2(COO)_4(M=Cu~(2+),Zn~(2+))units;(3)the infinite metal(such as Al~(3+),Ga~(3+) and In~(3+))oxide chains;(4)the hard metal(such as Cr~(3+),Fe~(3+),Ti~(4+),Zr~(4+),Hf~(4+),and rare earth metals)oxide clusters.The structure characters and stability have been described afterwards.The coordination bonds in the first and second types of SBUs are relatively weak.For comparison,most of the PMOFs based on the infinite metal oxide chains and hard metal oxide cluster exhibit high thermal/chemical stabilities,which could be used for practical applications towards C3.Then,we have summarized the recent works about applications of PMOFs in C3,which are divided into four parts,including the selective capture of CO_2,organic transformations with CO_2,CO_2 photoreduction and CO_2 electroreduction.Selective capture of CO_2 from a mixture of gases is one of the most important applications,considering that less energy and lower temperatures/pressures are required.Through the catalytic cycloaddition reaction of CO_2 and epoxides,the important products of cyclic carbonates can be produced.Some of the catalytic reactions can be carried out at 0.1 MPa and room temperature with high yields.With the assistance of environmentally friendly visible light,CO_2 can be photoreduced into fuels such as formate ion,methanol and methane.In addition,two typical examples of CO_2 electroreduction have been discussed in this review.Through the process of photoreduction and electroreduction,clean energies such as solar light and electricity can be employed to help transfer the green gas CO_2 into fuels.At the end,we have discussed the merits and challenges of PMOFs in the applications of C3.Selective adsorption of CO_2 from other gases,especially NO_x,SO_x and other flue gases,is highly required.The efficiency of the catalytic cycloaddition reaction should be further improved,especially cutting down the reaction time.Reaction efficiency and product selectivity of photoreduction and electroreduction should be improved.Photoelectrocatalytic reduction of CO_2,which combines both advantages of photoreduction and electroreduction,should be a hot topic in the future.The ideal system should include both a photoanode for water oxidation and a photocathode for CO_2 reduction that are linked by a wire without external applied bias,achieving the dream of artificial photosynthesis.