The exhaust stream from a lean-burn natural gas vehicle (NGV) typically has a maximum temperature of about 550 degrees C, a low concentration of methane (500-1000 ppmv) and a large amount of water vapor (around 15% by volume) which is a major cause of Pd catalyst deactivation. Such conditions pose significant challenges in the development of a small footprint catalytic converter to mitigate methane emissions. In this review, we address how the choice of support material can affect the Pd catalyst tolerance to water. Support hydrophobicity, its ability to serve as a sink for the hydroxyls, and oxygen mobility are some of the crucial factors that have contributed to improved catalyst stability and activity. In addition to the summary of the most recent advances in the field, we provide recommendations for catalyst testing and characterization techniques that are specific to the application of interest.