We are currently in the Cenozoic Era.
The Cenozoic Era, often referred to as the "Age of Mammals," is the most recent of the three Phanerozoic Eon eras. It is the geological era in which we currently live. The Phanerozoic Eon is further divided into three eras: the Paleozoic, Mesozoic, and Cenozoic. Knowing the approximate ages of the boundaries separating these eras is helpful for temporal reference Digital Atlas of Ancient Life.
In summary, the present-day era is the Cenozoic Era, marked by the prominence and diversification of mammals.
