Short answer
Using pleasant scent is a Sunnah, and burning aloeswood (oud) is reported from the Prophet's ﷺ own practice, so perfuming yourself, your clothes and your home with bakhoor is a good habit. Do not deliberately breathe in the smoke while fasting, since in the Hanafi school that breaks the fast.
Using incense and perfume is mustahabb, and scenting clothes, homes and mosques with bakhoor is good. Deliberately inhaling bakhoor smoke while fasting breaks the fast and requires a make-up day.
The four schools agree on this.
Explanation
Nafi' reported that Ibn Umar used to burn pure aloeswood, sometimes with camphor, and then said: this is how the Messenger of Allah ﷺ used to perfume himself with incense. He also described the people of Paradise, saying that their censers burn aloeswood. So burning oud is not only an Arab custom but part of the Sunnah of scent.
Aisha reported that the Prophet ﷺ ordered mosques to be built in the neighbourhoods and to be kept clean and perfumed. Many communities still scent their mosques with bakhoor on Fridays and in Ramadan, which follows this.
- Clothes and home: waft the smoke under your clothes or around the room. This is permitted and good.
- Fasting: in the Hanafi school, deliberately drawing the smoke into your nose or mouth breaks the fast. Light it after iftar, or stay away from the smoke; see smelling food or perfume while fasting.
- Safety: keep it away from children, smoke alarms and anyone with asthma, and air the room.
- Women going out: a strong bakhoor smell on clothes counts as perfume; see women and perfume.
For other scents, see is wearing perfume sunnah and is musk halal.
The evidence
Sahih al-Bukhari 3327
Sahih... أمشاطهم الذهب ورشحهم المسك ومجامرهم الألوة ...
"Their combs are of gold, their sweat is musk, and their censers burn aloeswood."
In describing the people of Paradise, the Prophet ﷺ praised aloeswood incense.
Sahih Muslim 2254
Sahih... استجمر بالألوة غير مطراة ...
"He perfumed himself with incense of pure aloeswood."
Ibn Umar did this and said it was how the Prophet ﷺ used incense.
Sunan Abi Dawud 455
Grading to be checked... ببناء المساجد في الدور وأن تنظف وتطيب ...
"He ordered mosques to be built in the neighbourhoods and to be cleaned and perfumed."
Scenting the mosque is part of the Sunnah.
Where the ruling is recorded
- al-Durr al-Mukhtar with Radd al-Muhtar, Kitab al-Sawm, chapter on what breaks the fast. Deliberately inhaling incense smoke breaks the fast.
- al-Fatawa al-Hindiyya, Kitab al-Karahiyya, chapter on perfume and adornment. Using perfume and incense is recommended.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.