Ungoliant, the first of the Spiders, was a Maiar, or so many believe. She may have been corrupted by Melkor Morgoth, but it is not known, for she served only herself. After she and Melkor Morgoth destroyed the Two Trees of Valinor, she returned to Arda and lived in Nan Dungortheb where she bred with other creatures, perhaps not even with Spiders. She devoured almost all of her children, yet some escaped.
Shelob was the largest of the children of Ungoliant. She fled to Mirkwood to escape the ruin of Beleriand, and there she reproduced. Her children were the smaller Spiders of Mirkwood, those that Bilbo encountered. For one reason or another, perhaps disappointed with the size of her offspring, she moved to Ephel D˙ath, and built for herself a den in the pass of Cirith Ungol. Here she would feast on Orcs or any other meat she could find. Sauron used her as a guard of this secondary entrance to Mordor, until she was dead, perhaps killed by Sam's attacks in the Third Age, or perhaps dying of hunger sometime during the Fourth Age.
During the Fourth Age, when Mirkwood became cleansed, the Spiders there, perhaps, tried to reproduce and reclaim the forest, but only the small Spiders we now know were produced. There are no Great Spiders left in the world.