The Rebbe's guidance on tznius (modesty) and on head covering — for married women, and for men and boys:
Modesty as a crown. Tznius is foundational for G-d's presence among the Jewish people and a defining trait of Jewish women (IK 9899, 9539). Torah values, modesty among them, are timeless and universal (IK 9640), and true modesty is rooted in the Torah received at Sinai (IK 1793). Strengthening modesty brings blessings of health, livelihood and true nachas (IK 2447). Education about tznius for women and girls should be a priority (IK 9852, 10253), and Anash women should take pride in visibly upholding chassidic standards of dress (IK 2970). Teachers' dress should reflect their values (IK 2834).
The sheitel. Head covering for married women is an explicit Torah obligation (IK 8953); only married women are required to cover their hair (IK 3592). The Rebbe strongly encouraged wearing a sheitel (IK 1892, 3053, 1432), which must cover all the hair (IK 2463, 2960). Wear it with joy and without embarrassment, even in the face of social pressure (IK 2434, 7425), and it brings clear blessing to the home (IK 2112, 2555, 7325). Insisting on a sheitel as part of a shidduch is proper (IK 5513). Be patient with changes in practice during pregnancy (IK 648).
Head covering for men and boys. Boys should have their heads covered from age three, from their first haircut (IK 2803), and a man's head covering, even before marriage, has halachic and spiritual significance (IK 8345).
In public life. Communal celebrations must keep halachic standards of modesty, including regarding women's singing at weddings (IK 8734). A proper mechitzah in shul is required (IK 2165). On mixed beaches, see IK 2992.
See also: Torah study – Women's Torah study; Marriage – Family purity and mikveh; Mitzvos in daily life – The beard and Jewish appearance.