Kali Yuga is the fourth and present age, of 432,000 years, in which dharma stands on one leg. The texts describe it in unsparing terms: rulers who plunder, teachers who sell knowledge, the collapse of family and of truth, short lives and small stature, and religion reduced to outward form. Traditional reckoning, following the astronomer Aryabhata and the Puranic sources, places its beginning at 3102 BCE, usually given as 18 February of that year, which leaves the great majority of it still to run; the age is not, on the traditional reckoning, anywhere near its end.
The name is from kali, the losing throw of one, and is unrelated to the goddess Kali, whose name is a different word with a different vowel. Modern reinterpretations that shorten the ages, notably that of Sri Yukteswar in The Holy Science (1894), are departures from the classical figures and should be identified as such.
Sources The Mahabharata and the Yugas: India's Great Epic Poem and the Hindu System of World AgesLuis Gonzalez-Reimann with Jyotihsastra: Astral and Mathematical LiteratureDavid Pingree