Generally, the eras used to describe the modern Earth are the Quaternary geological era and the Cenozoic evolutionary era. In the future, there may also be a historical era that the current time period, the 21st century, will belong to.
According to LiveScience.com, the Quaternary (fourth) geological era describes the most recent 2.6 million years, including modern times. It culminates into the Holocene Epoch, which describes the retreat of the glaciers and the last 12,000 years. According to UCMP Berkeley, the Cenozoic Era of evolution and animals describes the last 65 million years, from the extinction of the dinosaurs up until the modern day. It is sometimes called the "age of mammals."