The widespread utilization of fossil fuels has emitted large amounts of CO2 into the atmosphere since the Industrial Revolution, leading to climate warming and frequent occurrence of extreme climate events. To effectively alleviate climate change, the international community has made various efforts to reduce carbon emissions and eliminate CO2 from the atmosphere. In 2020, the Chinese government announced that carbon emission peaking and carbon neutrality will be achieved by 2030 and 2060, respectively. According to the current forecast, by the time carbon neutrality is achieved in 2060, even under the minimum conditions of fossil energy use, production, and living emissions, China will still have to emit about 1/4 of the current total emissions. These carbon must primarily be absorbed by ecosystems. Furthermore, approximately 140 ppm increase in CO2 in the atmosphere since the Industrial Revolution still needs to be removed by ecosystems. Forests are the main component of terrestrial ecosystems, contributing more than 80% of the carbon sequestration capacity of all terrestrial ecosystems. However, due to the long periodicity, complexity and dynamic variability of forests, the basic concepts of ecosystem carbon sink and its time effect are still unclear, leading to problems, such as lacking technologies for improving carbon sink capacity and disorganized rules in the carbon sink trading market. In this review, we introduced carbon sink concept according to the processes of absorbing and fixing CO2 by plant photosynthesis in forest ecosystems. Then, we analyzed the processes of time-scale-dependent carbon sinks of forest ecosystems, discussed the time effects of forest carbon sinks, and suggested using "t-year" as the unit of carbon sink (taking 3-6 months as the minimum measurement time, i.e., the beginning of carbon sequestration). Third, we proposed the approaches to improve the carbon sink capacity of forest ecosystems. One way is to improve the carbon sink capacity (expanding forest area, improving forest quality, and increasing forest soil carbon storage) of forest ecosystems. Another approach is to maintain the carbon sink of forest ecosystems as long as possible, i.e., to reduce temporary carbon sink (definition: carbon in the forest ecosystems emit into the atmosphere for a certain period) and to increase persistent carbon sink (definition: carbon in the forest ecosystems no longer emit into the atmosphere for a certain period; according to the relevant provisions of the Paris Agreement, the upper time limit for carbon sink measurement can be considered to be the year 2100. In order to maintain the persistent carbon sink, strateges such as efficient use of wood products (replace steel, cement, plastic with wood), control of forest fires or other disturbances-induced emissions, and turning forest biomass into biochar should be taken. Finally, we proposed to develop climate-smart forestry driven by artificial intelligence (AI), which would provide new theoretical and technical support for improving the carbon sink of forest ecosystems and facilitating sustainable forest management.