Atmospheric Methane (CH4) is the second most important greenhouse gas after carbon dioxide (CO2), and accounts for approximately 20% of the global warming produced by all well-mixed greenhouse gases. Thus, its spatiotemporal distributions and relevant long-term trends are critical to understanding the sources, sinks, and global budget of atmospheric composition, as well as the associated climate impacts. The current suite of hyperspectral thermal infrared sounders has provided continuous global methane data records since 2002, starting with the Atmospheric Infrared Sounder (AIRS) onboard the NASA EOS/Aqua satellite launched on 2 May 2002. The Cross-track Infrared Sounder (CrIS) was launched onboard the Suomi National Polar Orbiting Partnership (SNPP) on 28 October 2011 and then on NOAA-20 on 18 November 2017. The Infrared Atmospheric Sounding Interferometer (IASI) was launched onboard the EUMETSAT MetOp-A on 19 October 2006, followed by MetOp-B on 17 September 2012, then Metop-C on 7 November 2018. In this study, nearly two decades of global CH4 concentrations retrieved from the AIRS and CrIS sensors were analyzed. Results indicate that the global mid-upper tropospheric CH4 concentrations (centered around 400 hPa) increased significantly from 2003 to 2020, i.e., with an annual average of ~1754 ppbv in 2003 and ~1839 ppbv in 2020. The total increase is approximately 85 ppbv representing a +4.8% change in 18 years. More importantly, the rate of increase was derived using satellite measurements and shown to be consistent with the rate of increase previously reported only from in-situ observational measurements. It further confirmed that there was a steady increase starting in 2007 that became stronger since 2014, as also reported from the in-situ observations. In addition, comparisons of the methane retrieved from the AIRS and CrIS against in situ measurements from NOAA Global Monitoring Laboratory (GML) were conducted. One of the key findings of this comparative study is that there are phase shifts in the seasonal cycles between satellite thermal infrared measurements and ground measurements, especially in the middle to high latitudes in the northern hemisphere. Through this, an issue common in the hyperspectral thermal sensor retrievals were discovered that was unknown previously and offered potential solutions. We also conducted research on some applications of the retrieval products in monitoring the changes of CH4 over the selected regions (the Arctic and South America). Detailed analyses based on local geographic changes related to CH4 concentration increases were discussed. The results of this study concluded that while the atmospheric CH4 concentration over the Arctic region has been increasing since the early 2000s, there were no catastrophic sudden jumps during the period of 2008-2012, as indicated by the earlier studies using pre-validated retrieval products. From our study of CH4 climatology using hyperspectral infrared sounders, it has been proved that the CH4 from hyperspectral sounders provide valuable information on CH4 for the mid-upper troposphere and lower stratosphere. Future approaches are suggested that include: 1) Utilizing extended data records for CH4 monitoring using AIRS, CrIS, and other potential new generation hyperspectral infrared sensors; 2). Improving the algorithms for trace gas retrievals; and 3). Enhancing the capacity to detect CH4 changes and anomalies with radiance signals from hyperspectral infrared sounders.