Centuries: 21st century
The 100-year period from 2001 to 2100.
21st century: The 21st century is the period of 100 years from January 1, 2001, to December 31, 2100. We're living in it right now. A century is always counted from year 1 to year 100, which is why the 21st century started in 2001, not 2000 (even though many people celebrated the new millennium a year early).
When historians talk about the 21st century, they're describing the time we live in and the major changes happening around us: the rise of smartphones and social media, advances in artificial intelligence, new ways of generating energy, and the ongoing exploration of space. Future historians will look back at this century the same way we look back at the 20th century, studying what people accomplished, what challenges they faced, and how technology and society changed.
The tricky part about numbering centuries is that they're always one number higher than the year's first digits. The 1900s were the 20th century, the 1800s were the 19th century, and so on. This happens because there was no year zero: the calendar jumped from 1 BC to AD 1. So the first century was years 1 to 100, making our current century the 21st.