For an example, when they tried to get the carbon dating for presence of Aboriginal people in Australia they get to the number 40,000. But it could be much earlier. Why is that 40,000 years limit for carbon dating methods?
Carbon-14 makes up about 1 part per trillion of the carbon atoms around us, and this proportion remains roughly constant due to continual production of carbon-14 from cosmic rays. The half life of carbon-14 is about 5,700 years, so if we measure the proportion of C-14 in a sample and discover it's half a part per trillion, i.e. half the original level, we know the sample is around one half life or 5,700 years old.
So by measuring the C-14 level we work out how many half lives old the sample is and therefore how old it is. The trouble is that after 40,000 years there is under 1% of the original C-14 left, and it becomes too hard to measure it accurately. This isn't a fundamental limit as more accurate measurements could go further back, but at some point you'd simply run out of C-14 atoms. With our current kit 40-50K years is about the limit.