Yes, they do! The consistency of your cosmetics is charging over time, and they stop by being smooth and blendable as they should. Their molecules are breaking down and your skin, unfortunately, will react to it. In the best case will be just an irritation because it can lead to inflammation. Saving money by still using expired makeup products is not a good idea, at all!!
How to check when they are expiring? Check your cosmetics for the above icon! The number in the box it refers to months. Ex. This will expire in 12 months.