Rain Cap
The damage to the top of this older chimney is quite obvious. During the next windstorm it could be showering bricks.
Modern brick chimneys have rains caps made of concrete. These overhang the chimney to deflect water away from the bricks and mortar. Most older chimneys had a brick rain cap or none at all. Over the years moisture attacks both the mortar joints and the brick causing deterioration.
Some homeowners also compounded the problem by venting natural gas appliances into these unlined chimneys. It introduces another moisture source wetting the chimney from the inside.