1. Women are obligated to kindle Chanukah lights, because they were also involved in the miracle. When the husband is not at home, his wife may kindle with a blessing on his behalf, and he thereby fulfills his obligation through her kindling (Kitzur Shulchan Aruch, 139).
2. Chanukah lights are also kindled in the beis hakneses (synagogue) for the sake of publicizing the miracle of Chanukah, and blessings are recited over them. However, no-one fulfills their own obligation through these lights. The person honored to kindle in the synagogue must therefore light again in his home(ibid.). [It is customary to also kindle lights in the morning at the beis hakneses, without the blessings.]
