The laws of mourning apply to first-degree relatives: spouses, parents, siblings, and children. For the purposes of these halakhot, half-siblings (those who share only a common father or mother) are the same as full siblings.

A divorced man or woman is not classified as a mourner for an ex-spouse. They do not tear their garments nor sit shiva. Likewise, more distant relatives do not tear their garments nor sit shiva.

With that said, there are certain restrictions that apply to some relatives from the more distant family circle: the grandchildren of the deceased, a son-in-law, and a daughter-in-law. They should not participate in celebrations such as weddings while their parents or spouses are sitting shiva.

Further reading: For more on mourning, see A Concise Guide to Mahshava, p. 28.