Male modesty has been interpreted to be covering the area from the navel to the knee - and for women it is generally seen as covering everything except their face, hands and feet when in the presence of men they are not related or married to.
However, there has been much debate among Islamic scholars as to whether this goes far enough.
This has led to a distinction between the hijab (literally "covering up" in Arabic) and the niqab (meaning "full veil").
Hijab is a common sight among Muslim women, a scarf that covers their hair and neck.
Niqab consists of covering up completely, including gloves and a veil for the face - leaving just a slit for the eyes, or covering them too with transparent material.
Tell the faithful women to lower their gaze and guard their private parts and not display their beauty except what is apparent of it, and to extend their scarf to cover their bosom
Koran, 24:31 (English translation)
This form of dress is rarer, although it has been growing in recent years, and it is this which former UK Foreign Secretary Jack Straw says he objects to at face-to-face meetings with his constituents.
Muslim scholars have debated whether it is obligatory to don the niqab, or whether it is just recommended without being obligatory.
There have also been more liberal interpretations which say the headscarf is unnecessary, as long as women maintain the sartorial modesty stipulated in the Koran.
The holy text addresses "the faithful women" who are told to shield their private parts and not to display their adornment "except what is apparent of it".
Scholarly disputes revolve around what this last phrase means.
Find out about different styles of Muslim headscarf
Does it refer to the outer surface of a woman's garments, necessitating that she cover every part of her body - ie don the full niqab?
Or does it give an exemption referring to the face and the hands, as well as conventional female ornaments such as kohl, rings, bracelets and make-up?
The latter interpretation has been adopted by some of the most prominent scholars from Islamic history, such as Abu Jafar al-Tabari, who favour the hijab option.
There are additional Koranic instructions - seen as ambiguous and therefore much debated - for women to draw the "khimar" (or scarf) to cover the "jayb" (or bosom/upper chest), and for "the wives and daughters of the Prophet and the women of the believers to draw their "jalabib" (or cloaks) close round them".
Religious and cultural traditions vary across the Muslim world, stretching from Indonesia to Morocco.
But it may also be left to the Muslim woman to decide for herself, whether she wants to cover up fully with the niqab, as an expression of her faith and Islamic identity, or not.
In countries such as France and Turkey, where there are legal curbs on religious dress, it becomes a matter of women's human rights to wear what they want.
But at the same time the niqab is such a powerful statement that more liberal Muslims sometimes can be heard objecting to it, especially in more developed societies, where women have fought long and hard to shake off restrictions seen as outdated and imposed by men.