In recent years, there have been declines of varying severity in many vertebrate species across much of the sparsely populated savannas of northern Australia, and adding to the dismal record of extinctions from arid and semi‐arid central Australia since European colonization. It is likely that multiple factors are responsible for the current wave of extinctions, but they are occurring in areas of sparse human population in extensive, seemingly unmodified landscapes. Habitat change is one likely contributing factor, with invasive exotic grasses an important component in some regions. Historically, conservation of native vertebrates has been poor in Australia, with many species being considered vermin under legislation. As late as the 1960s much scientific research was aimed at controlling species that are now considered threatened under legislation. Through the 20th century substantial efforts to introduce exotic pasture species saw the introduction for trial of twice as many species of grasses and legumes as occur naturally on the whole Australian continent. The legacy of these programs is the spread of grasses that, through a range of processes, lead to simplification of floristic structure and reduction in plant species diversity and habitat suitability for many native mammals. Management of these invasive species should focus on preventing their spread into and establishment in new regions, and controlling them where they are established. State and transition models may provide a framework for considering the management and environmental triggers that could lead to re‐establishment of native grasses.