Reversibility of the binding of carbon monoxide to haemoglobin I recently learnt the basic mechanism of haemoglobin: oxygen forms coordinate bonds with the $\ce{Fe^2+}$ ion in haem groups, and this reaction is reversible to allow oxygen to be released. I also learnt that carbon monoxide does the same thing as oxygen, however, this reaction is said to be irreversible due to larger bond strengths etc. meaning that it can't be released.

What isn't clear to me is what happens to carbon monoxide if it does bind to a haem group. If the reaction is irreversible, then how is carbon monoxide removed from the body if you were to breathe it in?
The reaction is not irreversible, but hemoglobin adheres to $\ce{CO}$ about 200 times more tightly than it does to $\ce{O2}$. Thus, part of the treatment for $\ce{CO}$ poisoning is to expose the patient to oxygen, which will slowly displace $\ce{CO}$ from carboxyhemoglobin. 

For more on the chemistry involved, see this qestion.