Take a screwdriver or coin and run it along the mortar between bricks. Maybe it's obvious just looking at it. Rain puddles on the smoke shelf, mixes with creosote and becomes a corrosive liquid. It then seeps down and attacks the mortar between firebrick. The next step is loose brick.
Rain soaks into the chimney, freezes and splitting is the result.
Such a chimney becomes very weak with time. Rain will set off a bad smell during warm weather, especially if the chimney is dirty or there are bird droppings on the smoke shelf. If your fireplace is a metal box, with no cap, you can plan on replacing the unit in 5 to 10 years. With a wood stove or an insert in the fireplace, the result is the same only faster. A cap keeps out the birds, the squirrels, and the raccoons.