Modeling clay is a category rather than a product, and it contains materials that behave in opposite ways. Some never harden at all, by design. Some harden permanently at room temperature. Some are real ceramic bodies that harden only in a kiln. Buying the wrong one is the most common mistake on this shelf and the packaging is the only reliable guide.
The three kinds, plainly
Oil-based modelling clay, the plasticine kind, never dries. It stays workable indefinitely, which makes it ideal for animation, mould masters and practice, and useless for anything you want to keep. Water-based air drying clay hardens as it loses water and stays hard. Fireable ceramic clay hardens only when fired, and until then behaves like the air drying kind while being an entirely different material.
How to tell which you are holding
Oil-based clay does not stick to wet fingers and has a faintly waxy feel; it also does not soften with water. Water-based clays go sticky when wet and stiffen as they dry. If a packet says air drying, it hardens. If it names a firing temperature, it is a ceramic body. If it says neither, it is almost certainly the reusable oil-based sort.
What each is genuinely best at
Oil-based for anything iterative: a shape you will change repeatedly, a master for a mould, a stop-motion figure. Air drying for a keepable object with no kiln in the picture. Fireable clay for anything that will be used, washed or filled, because only firing produces a material that survives water. Choosing by task rather than by price avoids nearly every disappointment.
Price and where to buy
Craft shops sell all three in small packets at craft prices. Pottery suppliers sell air drying and fireable bodies by the bag at a fraction of the per-kilogram cost, which matters as soon as you are making more than one thing. The price index on this site compares fired bodies per kilogram excluding VAT, and the same suppliers list the air drying ranges beside them.
Questions people ask about modeling clay
Does modeling clay harden?
Some kinds do and some are designed never to. Oil-based plasticine stays soft indefinitely; air drying clay sets permanently; ceramic clay hardens only in a kiln.
Can modeling clay be fired?
Only if it is a ceramic body with a stated firing range. Oil-based clay must never go in a kiln.
Which is best for a child?
Reusable oil-based clay if the same material will be used again each week, air drying clay if each child takes their piece home.