Sheikh Muhammad bin Saalih al- Uthaimeen رحمه الله said:

One of the ways in which Allah has made things easy for His slaves is that He has only enjoined fasting upon those who are able to do it, and He has excused those who are unable to fast for a legitimate Sharr'i reason (Al-Mawsoo'ah al-Fiqhiyah, vol.28, pg.73)

The legitimate reason for which one may be excused from fasting are as follows:

Sickness

Sickness means everything that means that a person in not healthy. Ibn Qudamah رحمه االله said:

The scholars are agreed that it is permissible for the sick person not to fast in general.

The basis of that is the aayah in which Allah سبحانه وتعالى says:

 ...but if any of you is ill or on a journey, the same number (should be made up) from other days...  [Al-Baqarah 2:184]

it was narrated that Salamah ibn al-Akwa رضي الله عنه said when this aayah was revealed:

 And as for those who can fast with difficulty, (e.g. an old man), they have (a choice either to fast or) to feed a Miskeen (poor person) (for every day)  [al-Baqarah 2:184]

those who wanted no to fast could do that, and pay the fidyah (i.e., feed one poor person for each day).

That remained the case until the previous aayah was revealed so it abrogated it.

The sick person who fears that fasting may make his sickness worse or that it will slow down his recovery or damage a part of his body, has the option of not fasting, and indeed it is Sunnah for him not to fast and it is makrooh for him to complete his fast, because that may lead to his death. So, he has to be cautious and protect himself. Moreover, if the sick person is very ill, that makes it permissible for him not to fast. But if a healthy person fears difficulty or tiredness, it is not permissible for him to break his fast, if all that happens to him when he fasts is that he becomes tired.

Traveling

In order for traveling to result in a concession excusing one from fasting, the following conditions must be met:

 The journey must be long enough that prayers may be shortened.

 The Traveler must not intend to settle in the place to which he travels.

  His journey must not be for any sinful purpose, rather it should be for a sound purpose, according to the majority of scholars. That is because being allowed not to fast is a concession and relief that the sinner does not deserve on his journey, because the purpose of his journey is to commit sin - such as one who travels in order to commit banditry, for example Cancellation of the concession for traveling.

This concession of traveling is cancelled by two things:

 When the traveler returns home and enters his hometown, which is the place where he resides.

 When the traveler decides to stay indefinitely, or for a lengthy period in one place, and the place is fit for settling in. Thus he becomes a resident ( or non-traveler ), so he should pray his prayers in full and not break his fast in Ramadhan, because the rulings on travel no longer apply to him.

Pregnancy and Breastfeeding

The Fuqaha agreed that pregnant and breastfeeding women may break their fast in Ramadhan, on the condition if they think there is a risk that they or their children may become ill, or be harmed or may die.

The evidence for this concession in their case is the aayah:

 and whoever is ill or on a journey, the same number [of days which on did not observe Sawm (fasts) must be made up] from other days... [al-Baqarah 2:185]

This does not refer to merely being sick, for the sick person who will not be harmed by fasting is not allowed to break the fast; here sickness is mentioned as metaphor for any situation where fasting when sick may cause harm. This what is meant by sickness here. That may be the case in pregnancy and when breastfeeding, so these two cases are included in the concession of breaking the fast.

The evidence that women in these cases are allowed not to fast is the hadeeth of Anas ibn Malik al-Ka'bi رضي الله عنه , who said that the Messenger of Allah صلى الله عليه وسلم said:

 Allah has relieved the traveler of fasting and half of prayer, and He has relieved the pregnant and breastfeeding women fasting. 

Senility and old age

Senility and old age refers to one who is old and has lost his strength, or who is approaching death, so that every day he becomes weaker, until he dies, or who is suffering from a terminal or incurable illness and has no hope of recovery.

The evidence that it is prescribed for such people not to fast is aayah:

 And as for those who can fast with difficulty, (e.g. an old man), they have (a choice either to fast or) to feed a Miskeen (poor person) (for every day). [al-Baqarah 2:184]

Ibn Abbas رضي الله عنه said that this aayah has not been abrogated, and it applies to old men and old women who cannot fast, so for each day they should feed one poor person.

Intense Hunger and Thirst

If a person is overtaken by intense hunger or unbearable thirst, then he should break his fast and eat just as much as he needs to ward off that hunger, then he should refrain from eating for the rest of the day, and make up that fast later on.

The scholars added to intense hunger and thirst the fear of weakness when meeting the enemy, or fearing or expecting an attack, such as when one is surrounded. So, if a fighter knows for sure or thinks it most likely that there will be fighting because he is facing the enemy, and he fears that fasting may make him weak when fighting, and he is not traveling, then he may break his fast before fighting.

Compulsion

Compulsion means one person forcing another to do something or not to do something against his will by means of threats.