Final answer:
The current epoch within the Cenozoic Era is the Quaternary, representing the modern geological time period and the age of mammals.
Step-by-step explanation:
Our current epoch geological time period within the Cenozoic Era is called the Quaternary. The Quaternary is the current and most recent of the three periods of the Cenozoic Era, spanning from about 2.588 million years ago to the present. The Cenozoic Era itself is known as the era of "modern life" or the age of mammals, beginning about 65 million years ago and continuing into the present. Major events in this era include the flourishing of mammals after the extinction of the dinosaurs and significant ice ages during the Quaternary Period.