Chimney Liners - Essential to keep your fire safe
Chimney liners are necessary for ill fitting or leaky flues
The point of chimney liners is the same as the point of chimneys themselves - to make your fire safe. A chimney conveys the unwanted byproducts of a fire from your room to the outdoors. It works because hot air, and any fumes or smoke it may carry with it, rises (also the reason you should keep close to the ground if you are unlucky enough to be caught in a house fire).
That means that the flue (the inner part of the chimney) needs to be the right size for your fire and structurally sound. If the chimney is too large or too old it may let cold air into the flue, affecting the upward progress of hot air, fumes and smoke from the fire. In the case of leaky or ill fitting flues, chimney liners are necessary.
In 1965 a law was passed stipulating that all new flues had to be built with liners. So it's in houses built before this date where many flue problems arise. Then, the resilient clay lining which is most popular now was not used - instead, chimneys were 'parged' with lime mortar which it turned out was susceptible to gradual corrosion by the gases released by fires. That caused leakages into any available spaces in the house - particularly dangerous in the case of highly toxic carbon monoxide fumes. That's not to say it's only in houses built in the 1960s and before where there are problems, though. Bad workmanship can render any flue dangerous.
The dangers of carbon monoxide poisoning in particular are real and not to be taken lightly. The integrity of chimney brickwork can be examined in detail with a pressure smoke test, and if you have doubts about the age or health of your chimney you should have this done - as any reputable dealer will advise you. The type and thickness of lining will depend on where in the house the chimney is (proximity to an outer wall this contributes to cooling) and the type of fuel you use. And the more storeys the chimney reaches up, the more expensive it will be to have it lined. But if you want a fire, it's essential to make sure it's safe.