About chimney tuck-pointing
A chimney with damaged bricks and mortar needs to be repaired. The process of repairing these issues is called tuck-pointing and involves replacing the bricks and placing new mortar. Damaged bricks are dangerous because they may fall off the chimney and they also cause leaks that may allow external elements to enter your house.
Sometimes, chimneys can be so damaged that the process of tuck-pointing may be impossible and useless. In this case you will have to demolish you chimney to its most stable point and reconstruct it.
Before beginning the tuck-pointing process, you must remove any loose debris like damaged bricks and mortar. This way, the new layer of mortar will have a stable foundation to stick to.
As a last step, you must keep the tuck-pointed area moist for a several days to assure that it will dry slowly and will not crack and break when used.