I'm asking this since there's a range of "coverage" that we see in Muslim women, from the niqab which covers everything except for the eyes to a headscarf that covers just the head and not the neck/chest area, and other variations.
It is mandatory that women wear cloths that cover their whole bodies. But since this question is about Hijab. Allah tells us in the Qur'an:
وَقُل لِّلۡمُؤۡمِنَـٰتِ يَغۡضُضۡنَ مِنۡ أَبۡصَـٰرِهِنَّ وَيَحۡفَظۡنَ فُرُوجَهُنَّ وَلَا يُبۡدِينَ زِينَتَهُنَّ إِلَّا مَا ظَهَرَ مِنۡهَاۖ وَلۡيَضۡرِبۡنَ بِخُمُرِهِنَّ عَلَىٰ جُيُوبِہِنَّۖ وَلَا يُبۡدِينَ زِينَتَهُنَّ إِلَّا لِبُعُولَتِهِنَّ أَوۡ ءَابَآٮِٕهِنَّ أَوۡ ءَابَآءِ بُعُولَتِهِنَّ أَوۡ أَبۡنَآٮِٕهِنَّ أَوۡ أَبۡنَآءِ بُعُولَتِهِنَّ أَوۡ إِخۡوَٲنِهِنَّ أَوۡ بَنِىٓ إِخۡوَٲنِهِنَّ أَوۡ بَنِىٓ أَخَوَٲتِهِنَّ أَوۡ نِسَآٮِٕهِنَّ أَوۡ مَا مَلَكَتۡ أَيۡمَـٰنُهُنَّ أَوِ ٱلتَّـٰبِعِينَ غَيۡرِ أُوْلِى ٱلۡإِرۡبَةِ مِنَ ٱلرِّجَالِ أَوِ ٱلطِّفۡلِ ٱلَّذِينَ لَمۡ يَظۡهَرُواْ عَلَىٰ عَوۡرَٲتِ ٱلنِّسَآءِۖ وَلَا يَضۡرِبۡنَ بِأَرۡجُلِهِنَّ لِيُعۡلَمَ مَا يُخۡفِينَ مِن زِينَتِهِنَّۚ وَتُوبُوٓاْ إِلَى ٱللَّهِ جَمِيعًا أَيُّهَ ٱلۡمُؤۡمِنُونَ لَعَلَّكُمۡ تُفۡلِحُونَ (٣١)
Translation (interpretation of meaning):
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 (ordinarily) appear thereof; that they should draw their veils over their bosoms and not display their beauty except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, or their brothers' sons, or their sisters' sons, or their women, or the slaves whom their right hands possess or male servants free of physical needs, or small children who have no sense of the shame of sex; and that they should not strike their feet in order to draw attention to their hidden ornaments. And O ye Believers! Turn ye all together towards Allah that ye may attain Bliss. (31)
Surat 24 Ayah 31
From this Ayah we get that Women should at least have the Hijab covering their heads to as the Ayah says, bosoms.
Abu Dawood narrates:
Asma, daughter of AbuBakr, entered upon the Messenger of Allah (sallallahu 'alaihi wa sallam) wearing thin clothes. The Messenger of Allah (sallallahu 'alaihi wa sallam) turned his attention from her. He said: O Asma', when a woman reaches the age of menstruation, it does not suit her that she displays her parts of body except this and this, and he pointed to her face and hands.
graded as Saheeh
Allah says in the Holy Quran Chapter 33 Surah Al Ahzaab verse 59:
O Prophet! Tell your wives and daughters, and the women of the believers, that they should cast their outer garments over their persons. It is expected that they will be recognized and that they will not be molested. And Allah is Oft Forgiving, Most Merciful.
Allah says in the Holy Quran Chapter 24 Surah An-Noor verse 31:
And O Prophet, enjoin the believing women to restrain their gaze and guard their private parts and not to display their adornment except that which is displayed of itself (their face and hands), and to draw their veils over their bosoms and not to display their adornment except before their husbands, their fathers, the fathers of their husbands, their sons and the sons of their husbands, their brothers, their brothers sons, their sisters’ sons, their female associates, and those in their possession and male attendants incapable of sexual desire, and those boys who have not yet attained knowledge of sexual matters. Also forbid them to stamp their feet on the ground lest their hidden ornaments should be displayed.
You can infer from the second para that Hijab should cover a woman from head to bosom. But it doesn't mean that it stops at the bosom. Hijab goes till toes.
This relevant to the Twelver Shiite school.
An adult/pubescent lady can only keep her face and hands uptil the wrist uncovered while observing the Islam Hijab. Otherwise every part of her body should be covered, including the hair.
To elaborate, face here includes the region between the forehead (included), and the area below the chin that is visible when a headscarf is worn (not the neck). And does not include the ears. No part of the arms should be left uncovered.
From Grand Ayatullah Sayyid Ali Husaini Sistani:
Question: A vast majority of Muslim women who observe hijãb are used to keeping their chins and a small part of the under chin exposed but they cover the neck. Is this permissible for them? And how big an area of the face women can expose? And are the ears included in that?
Answer: The ears are not part of the face, therefore it is obligatory to cover them. As for the part of the chin and the under chin that are seen when putting on the common head scarf, it is to be considered as part of the face.
A woman should not show her beauty or adornments except what appears by uncontrolled factors such as the wind blowing her clothes