It is extraordinary that we've found a way to figure out the age of materials. I'm noting a few techniques that I encountered while reading and will update when I find newer ones.
Organic materials containing carbon can be dated via this method. is a mild radioactive isotope that accumulates in a dead organism. is naturally created in the atmosphere by the interaction of nitrogen with cosmic rays. The decay of radioactive material is described by half-life - the time required for a material to be reduced to half of its initial value. The half-life of is about 6000 years. Owing to this, there is a limit to how far back we can reliably date using this method (50,000 years in this case).
The key idea behind this luminescence dating starts under a similar premise but goes beyond organic materials. Soils usually contain traces of radioactive isotopes of elements. The ionizing radiation produced by these isotopes gets trapped in buried quartz (silicon) and feldspar (potassium silicates) in unstable electron traps between the crystalline structure. When exposed to light, the stored energy is released in the form of luminescence and measuring this is related to the total time electrons were trapped in the crystals.
Under the correct conditions, optically stimulated luminescence (OSL) dating can reliably estimate upto 350,000 years.