The atmospheric CO_2 concentration has recently exceeded 400ppmv, which deepens the concern of a potentially accelerated global climate change. To understand the relationship between climate change and atmospheric CO_2 concentration, the past is the key. In this paper, we collect and analyze past 500Ma records of atmospheric CO_2 concentration and temperature in eight time periods, namely Phanerozoic, Mesozoic, Cenozoic, middle Pleistocene, last deglaciation, Holocene, past millennium, and recent decades. According to the information carriers and time spans,we divide these records into three categories:(1) The millionaire and longer records from model calculation and paleosols or paleobotany proxies:Although the trends of the changes in atmospheric CO_2 concentration and temperature are generally consistent on this time scale,it is difficult to establish a clear causal relationship because of the great uncertainties and low resolutions of both sets of data. (2) The orbital scale records mainly from the polar ice core:High precision atmospheric CO_2 concentration and temperature reconstructions allow for an examination of the possible role of atmospheric CO_2 in the process of glacial-interglacial transformation. However, no definite causal relationship has been found. (3) The records at centennial and shorter time scales over the past millennium from ice,snow,and the instrumental data:The records are the most abundant and of highest resolutions. Moreover, there are instrumental records of atmospheric CO_2 concentrations over the recent decades. However, due to the difficulties in distinguishing the effect of the greenhouse CO_2 from other climatic factors, there are great uncertainties in the interpretation of climate change versus atmospheric CO_2 concentration. Overall, this paper comes to the following major conclusions:(1) Paleoclimate reconstructions show that global surface air temperature and atmospheric CO_2 concentration have generally decreased over the past 500Ma. However, there is no consistent sequential order in the changes between these two variables. (2) The Earth's atmospheric CO_2 concentration has a drastic fluctuation history. There were many carbon-enriched periods when atmospheric CO_2 concentration were as high as greater than 5000ppmv; whereas there were relatively fewer carbon-depleted periods when atmospheric CO_2 concentration dropped to as low as smaller than 200ppmv. (3) According to the world-wide observational data, atmospheric CO_2 concentration has recently exceeded 400ppmv. Although there is no conclusive evidence to show that this CO_2 concentration value bears any significant climate consequences, it is the highest since the last 800ka,and rare over the Quaternary (2.58Ma).