Current Kali Yuga and possible starting and ending dates
According to the Surya Siddhanta, Kali Yuga began at midnight (00:00) on 18 February 3102 BCE.
This is also considered the date on which Lord Krishna left the earth to return to Vaikuntha. This information is placed at the temple of Bhalka, the place of this incident (see photo).
Information kiosk at Bhalka
, the place from where Lord Krishna returned to his heavenly abode
According to the astronomer and mathematician Aryabhatta the Kali Yuga started in 3102 BCE. He finished his book "Aryabhattiyam" in 499 CE, in which he gives the exact year of the beginning of Kali Yuga. He writes that he wrote the book in the "year 3600 of the Kali Age" at the age of 23. As it was the 3600th year of the Kali Age when he was 23 years old, and given that Aryabhatta was born in 476 CE, the beginning of the Kali Yuga would come to (3600 - (476 + 23) + 1 (As only one year elapses between 1 BCE and 1 CE) = ) 3102 BCE.
According to KD Abhyankar, the starting point of Kali Yuga is an extremely rare planetary alignment, which is depicted in the Mohenjo-Daro seals. Going by this alignment the year 3102 BCE is slightly off. The actual date for this alignment is 7 February of 3104 BCE. There is also sufficient proof to believe that Vrdhha Garga knew of precession at least by 500 BCE. Garga had calculated the rate of precession to within 30% of what the modern scholars estimate.
The common belief until Swami Sri Yukteswar Giri had analyzed the dating of the Yuga cycles was that the Kali Yuga would last for roughly 432,000 years after the end of the Dwapara Yuga (3102 BCE). This originated during the puranic times when the famous astronomer Aryabhatta recalculated the timeline by artificially inflating the traditional 12,000 year figure with a multiplication of 360, which was represented as the number of "human years" that make up a single "divine year". This was likely a purposeful miscalculation due to conflicts with one of the preeminent astronomer of the time Brahmagupta. However, both the Mahabharata (which was used by Aryabhatta in his calculations) and the Manu Smriti have the original value of 12,000 years for one half of the Yuga cycle.
Contemporary analysis of historical data from the last 11 millennia matches with the indigenous Saptarishi Calendar. The length of the transitional periods between each Yuga is unclear, and can only be estimated based on historical data of past cataclysmic events. Using a 300 year (10% of the length of a particular yuga) period for transitions, Kali Yuga has either ended recently in the past 100 to 200 years, or is to end soon sometime in the next 100 years.
Other authors, such as the revered Hindu guru Swami Sri Yukteswar in his book The Holy Science, as well as the influential Yogi Paramhansa Yogananda, believe that the Kali Yuga has already ended, and that we are now in an ascending Dvapara Yuga. This calculation is also supported  by modern day spiritual masters such as Sadhguru Jaggi Vasudev.