Adherents of Islam are concerned with clothing in two contexts: clothing for everyday, inside and outside the house, and clothing required in specifically religious contexts.

“ Say to the believing men that they should lower their gaze and guard their modesty: that will make for greater purity for them: And Allah is well acquainted with all that they do. ”

Qur'an [24:30]
“ And say to the believing women that they should lower their gaze and guard their modesty that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their veils over their bosoms ... ”
Qur'an [24:31]

“ O Prophet! Tell thy wives and thy daughters and the women of the believers to draw their cloaks close round them. That will be better, so that they may be recognized and not harassed. Allah SWT is ever Forgiving, Merciful. ”
Qur'an [33:59]

However, there are many different interpretations of what "modesty" requires. Most agree that it is covering the "awrah", from the belly button to the knees for men and from the head to the toes for women except the face and hands.