Hi:

I noticed lately a musty smell and upon further investigation I found black marks on drywall which seem to start from the concrete floor and move up wall 1/2 way. What is this, is it dangerous to health and how do I get rid of it? Please offer suggestions. This bothers me a lot.

From the sounds of it you have mold. And this is best evaluated by a professional. Some molds can be dangerous to your health. This needs to be addressed right away.

Yes, you are experiencing mold problems and that is happening due to a combination of two things:
1 - Ground water seeping through the concrete slab and walls, through capillary action, through the joint between the wall and the floor, or through cracks in the foundation.

2 - Presence of organic matter on the drywall, fiberglass and wood studs. When organic materials come in contact with water, they absorb it and create conditions for mold to develop. Mold feeds on organic matter.

Regardless of the species you are dealing with, all mold is bad news and the U.S. Center for Disease Control and the U.S. Environmental Protection Agency urge you to get rid of it.

Although only a few species are toxic, all mold release spores which can trigger allergy symptoms in sensitive people. In addition, if you don't get rid of it right away, it will eventually become bigger and may spread to rooms upstairs.

If the infestation is bigger than 10sq feet (roughly a 3ft by 3ft area)the EPA urges you to contact a professional mold remediation company as only they have the proper knowledge and gear to deal with it.

If it is just a small infestation, you can clean it yourself by using the EPA's mold cleanup guidelines.

All the contaminated drywall, fiberglass, wood and carpet will need to be removed and discarded as there is no way to safely remove mold from these surfaces. You might need then to wipe or scrub the concrete clean.

While you are at it, check for the source of this moisture. You might need to improve drainage to stop leaks with an interior drain tile.

Considering replacing your basement flooring and walls with waterproof and inorganic tiles, laminates and wall panels instead of wood, carpet and drywall.

A dehumidifier, used to keep relative humidity levels at or below 55% will keep your basement dry and mold free.