It often happens that when one error is corrected, another one surfaces on the opposite side of the spectrum. The Council of Ephesus in 431 took on the Nestorian heresy, which despite the intentions of its advocates, had divorced Christ's two natures so crassly as to effectively leave Him with a duality of persons. One of the more famous implications of this mode of thinking was that it was impossible for a Nestorian to call Mary the "Mother of God." A mere twenty years after Ephesus the opposite problem had to be addressed, viz., that of monophysitism, its chief advocate being Eutyches. Under this heresy, Christ's natures are not merely united in one hypostasis, but blended into one nature.
The Church's Christology is beautifully rounded out with the clarification of Chalcedon. Ironically, one cannot really discuss this council without mention of a man who was absent, and yet was a key player. This is of course Saint Leo the Great. Pope Leo did not attend, but sent a few representatives instead, and with them a few letters, amongst which was the so called Letter to Flavian, the archbishop of Constantinople. This letter became known as Saint Leo's Tome, and effectively guided the debate. The Letter has both a Latin and a Greek history, and exists in many translations today. The one with which I am most familiar is from the old 19th century vintage Nicene & Post Nicene Fathers series, which is even online now, probably in many different places on the web. Here is one such source. If you can, take a moment to read it over today. This is our Leonine, and Chalcedonian heritage.