Few questions in this territory produce more confident and more contradictory answers online. The honest answer has two parts, because the tradition itself holds two systems.
The Puranic arithmetic
The classical scheme (laid out in Manusmriti 1.68–71 and the Puranas) counts four ages in divine years, where one divine year is 360 human years: Satya 4,800 divine years, Treta 3,600, Dvapara 2,400, Kali 1,200 — in human years, 1,728,000 / 1,296,000 / 864,000 / 432,000. Tradition dates the Kali Yuga's start to the passing of Krishna, fixed by the astronomer Aryabhata's school at 3102 BCE. On that arithmetic, roughly five thousand years have passed and well over four hundred thousand remain. The age is, by its own account, in its infancy.
The Yukteswar reinterpretation
In The Holy Science (1894), Sri Yukteswar — teacher of Paramahansa Yogananda — argued the divine-year multiplication was a later misreading, and proposed a 24,000-year cycle of ascending and descending ages tied to a slow astronomical motion. On his scheme the darkest point lay around 500 CE, and humanity is now in an ascending Dvapara — an age of increasing energy and knowledge. His system has real influence in modern yoga lineages, and its optimism is part of the appeal; it is also, it should be said, a nineteenth-century reinterpretation, not the Puranic text.
Why the viral dates fit neither
Posts announcing that "the Kali Yuga ends in 2025" (or 2032, or whenever the video was made) belong to neither system: the Puranic clock has hundreds of millennia to run, and Yukteswar's has no ending-event in this century at all. They usually trace to numerological reworkings or to misread claims about specific texts. Whatever their sincerity, they demonstrate the one safe rule in this field: when a specific modern date is attached to an ancient text, the date is modern.
The more useful question
The texts that describe the age's faults are less interested in its end-date than in conduct within it — the Bhagavata's own conclusion is that this age offers the easiest path of any (see the full passage). For time as the traditions actually measure it — living, observable time — our festival calendar computes the real lunar months, and the panchang's daily yogas turn with the actual sky.
Related
The four ages, twice discovered · Kalki: what the texts say · Today’s panchang