Radioactive Dating
Because a radioactive isotope decays at a rate fixed by its half-life, the ratio of leftover "parent" atoms to the "daughter" atoms they turn into acts like a stopwatch: measure the ratio, and you read off how long decay has been running.[1] With isotopes whose half-lives run to billions of years (uranium-lead, potassium-argon), this radiometric dating pins the age of rocks — the oldest Earth minerals at ~4.4 billion years, and meteorites at 4.57 billion, which sets the age of the Solar System on the cosmic timeline.[2] It's also how the layers around a fossil get their dates. For recent, once-living material, the go-to method is carbon dating.
Each half-life, half of what's left decays — so after 1 it's 50%, after 2 it's 25%, and so on. For carbon-14 (half-life 5,730 years) that's an age of about 5,730 years; other isotopes with longer half-lives reach back billions.