A headstone (tombstone) is known as a matzevah ("monument"). Although there is no Halakhic obligation to hold an unveiling ceremony, the ritual became popular in many communities toward the end of the 19th century.
There are varying customs about when the matzevah should be placed on the grave. Most communities have an unveiling ceremony a year after the death. Some communities have it earlier, even a week after the burial. In Israel it is done after the "sheloshim", the first thirty days of mourning. There is no restriction about the timing, other than the unveiling cannot be held during certain periods such as Passover or Chol Ha'Moed.
At the end of the ceremony, a cloth or shroud covering that has been placed on the headstone is removed, customarily by close family members. Services include reading of several psalms (1, 23, 24, 103), Mourners Kaddish (if a minyan is available), and the prayer "El Malei Rachamim." The service may include a brief eulogy for the deceased.