Influenza A H1N1/2009 virus that emerged from swine rapidly replaced the previous seasonal H1N1 virus. Although the early emergence and diversification of H1N1/2009 is well characterized, the ongoing evolutionary and global transmission dynamics of the virus remain poorly investigated. To address this we analyse >3,000 H1N1/2009 genomes, including 214 full genomes generated from our surveillance in Singapore, in conjunction with antigenic data. Here we show that natural selection acting on H1N1/2009 directly after introduction into humans was driven by adaptation to the new host. Since then, selection has been driven by immunological escape, with these changes corresponding to restricted antigenic diversity in the virus population. We also show that H1N1/2009 viruses have been subject to regular seasonal bottlenecks and a global reduction in antigenic and genetic diversity in 2014.