The next upcoming Muharram starts on sundown of Thursday August 20th, 2020.
Some Muslims will fast during the month of Muharram which is one of the four sanctified months on the Islamic calendar. Many will pray especially on the 10th day of the month called Ashura in which fasting is done and martyrdom is honored by Muslims. Many will also give to charity and the poor on the Islamic New Years day.
Muharram is the first month of the Islamic lunar calendar which contrast to the west using the Gregorian solar calendar. Thus both calendar systems have a different day for the New year depending on the solar or lunar positioning in the sky.