It is an odd thing that the first page of the Shulchah Aruch, the binding code of Jewish Law, devotes space to a custom that most observant Jews today do not follow. Tikkun hatzot is the practice of rising in the middle of the night to pray and lament over the destruction of the Temple and the continuing exile of the Shechinah, the Divine Presence.
There is a service for tikkun hatzot, which until the early 20th-century was printed in most siddurim. The custom is to stay awake subsequently studying Torah, if possible until morning services at dawn. The Shulchan Aruch writes "It is right that all who fear God should be pained and troubled about the destruction of the Temple." When then do you sleep? The Shulchan Aruch apparently assumes that you will figure that out for yourself.
In his book about tikkun hatzot, The Sweetest Hour, Rabbi Avraham Greenbaum writes movingly about the "exquisite grace and beauty" of this hour as a time for prayer, meditation and contemplation. With the rise of neo-Chasidism. Tikkun hatzot is making something of a comeback among spiritual seekers. As Greenbaum says, it is not an obligation, but rather an act of love.