By the lunar Fatimid calendar, today (Saturday 28th June) is the 1st of Ramadan. The Mecca-centric calculations of The Fiqh Council of North America (affiliated with the Islamic Society of North America) also concur with the lunar calendar in declaring today the 1st of Ramadan.
Most moonsighting communities have not yet confirmed a positive moon sighting, according to Moonsighting.com and according to CrescentWatch.org. For communities that adhere to the moonsighting tradition, Ramadan begins tomorrow on Sunday, 29th June.
Whether you begin fasting today or tomorrow, Ramadan Mubarak! Please do remember me and my family in your precious dua.
Related: my contribution to the moonsighting debate, where I argue that calculations are just as valid as moonsighting and rebut some of the exclusivity arguments that moonsighters sometimes make (not to mention pointing out that moonsighters themselves also use calculations). Also, Dr. Muqtedar Khan has written a new essay in favor or calculations that is very thought-provoking, On the moon-sighting debate: a Maslaha-based argument.. Finally, an old brief essay of mine of some relevance: in motion, the believers reflect the heavens.