It isn't what one might call a scholarly, factual work, but the Odyssey begins with Poseidon "on a visit to the distant Ethiopians, in the most remote part of the world, half of whom live where the Sun goes down and half where he rises". I am unsure whether this means Homer believed the Ethiopians to have a huge nation spanning from West to East, or he believed all sub-Saharan Africans to be Ethiopians, or any other interpretation, but I hope it helps.

Homer, The Odyssey (E.V. Rieu translation, Penguin Classics) pp 3

Good question, and a difficult one. Trans-Saharan contact is a pretty big topic right now, but unfortunately it is one with a fatal gap of evidence. Other people here have mentioned the trade with India, which is my personal specialty, and that makes a rather intriguing parallel. The problem is that our sources, in practically every way, are significantly better for India than for sub-Saharan Africa. Classical sources mention India far more (due to the connection with Alexander), India has a very large body of surviving literature that can be drawn on, and archaeological research within the subcontinent is significantly older than that of sub-Saharan Africa. So while these are similar, there is a fundamental difference in source evidence that is both entirely to the advantage of India but is not necessarily reflective of a real difference in contact.

Broadly speaking, the "backbone" of our knowledge of the ancient Saharan trade is funded upon the Medieval equivalent and traditionally there has been seen a linear temporal progression, ie, the ancient trade fed into the larger Medieval trade. But scholars such as Andrew Wilson have recently contested this, arguing that it is quite possible the Roman trade was actually larger. A fundamental piece of evidence for this is found within the Sahara itself, which due to geological luck was more densely settled in the Roman period than it was in any period before or since until the twentieth century. This was because during the Roman period there were a large number of large, underground water reservoirs that could be tapped by the native Berber people called "Geramantes" through an irrigation system called foqqara, which could be used to support an agricultural base of urbanization where today there is only sand. The decline of this reservoir may have been due to overuse, or perhaps to climate change or geological processes, but either way particularly in the Fezzan there was a large body of underground water that could be tapped then that cannot today.

The Geramantes, then seem to have been the drivers of a camel-based caravan trade linking Roman North Africa to around Lake Chad. the actual goods carried on this are rather difficult to know. Wine, grain and carbuncles may have been exported from Rome, and from comparison to Medieval trade salt, gold, and slaves may have been imported. But it really isn't well known, unlike the extensive product lists we have for India. Another question is how far down this trade went, and there is intriguing evidence in the form of pottery found in Geramantes sites from the heavily urbanized region of the Niger River. Unfortunately, our knowledge of this region is extremely poor, not having the advantage of the extensive archaeology seen in North Africa. It is likely, almost certain, that new excavation will reveal new and exciting data for this surprisingly interconnected world.

The two best introductory articles I know on this are Andrew Wilson's "Saharan trade in the Roman period: short-, medium- and long-distance trade networks" and Katia Schorle's "Saharan trade in Classical Antiquity".

Western Sub-Saharan had contact contact with the Muslim world before the Christian world I believe. Hence Mansa Musa being a Muslim.

However, western civilization was quite aware Eastern Sub-Saharan Africa and the Christian kingdoms in Ethiopia. If I recall correctly the legendary Prester John was believed to be in Ethiopia because Europeans were aware that there were Christian kingdoms there.

Well Indeed the Romans and Ptolemaioi did have naval/trading contacts and a brief military episode with the Ethiopians. The Naval contacts of both and how far they reached (both directly and indirectly) might be a little up to debate. The Periplus of the Erythraean Sea is probably the best source on the knowledge of the Romans of South East Africa.

The West has not been covered as much. Probably due to the pastoral lifestyle of their neighbours in the area, whereas modern Yemen, and Ethiopia was home to settled and reasonably centralized kingdoms. Perhaps more importantly both were fabled for their riches and sources. (Incense, gold, Ivory, medicines, precious stones and important trade connections with India and Sri Lanka (Cinnamon).

However the West was certainly explored as well, at least to some extent. However not as much by the Hellenes or Romans, rather by the Carthaginians. Hanno the navigator for one was a king famous for his travels along the West Coast of Africa.

Pomponius Mela, the Roman Geographer who wrote De Chorographia in 43 AD, really didn't know what was in Sub-Saharan Africa. He described this far off land as a place filled with mythological beasts, antichthones, and also considered the extreme south to be so hot that humans couldn't inhabit it.

Well, the Egyptians didn't go much further west than Libya, but for most of Dynastic Egypt they conquered down the Nile into Nubia, which is modern day Sudan. They also traded extensively down the coast of the Red Sea to an area known as Punt, the location of which is unknown today but is probably somewhere around Somalia. They needed this trade for materials used in the mummification process which were not native to Egypt. Stuff like leopard skins, frankincense, and myrrh.