What calendar is currently used for judaism?

Judaism has its own unique calendar which is a luni-solar calender where every month is a lunar month, but the years change length to coordinate roughly with a solar year (354 and 384 days) and become equivalent after 19 years. This calendar in its present form dates back to 360 CE; before that, the New Moon was declared following the testimony of witnesses..

The Jewish calendar consists of twelve lunar months. It also keeps in step with the solar year, by adding a thirteenth lunar leap-month seven times every nineteen years.

The Gregorian calendar, which sticks to the solar year, ignores the lunar months and does not attempt to keep in step with them.