fasting is obligatory on the mature sane and healthy muslim. those who are immature (i.e. little children) are encouraged to fast. exempted are those who suffer terminal illness, or are too old to fast. allah does not overburden his slaves.

on the other hand, permission to abstain from fasting is granted to the travelers who do not travel for the purpose of breaking their fast. even though it is permissible to break fast during travel, yet it is praiseworthy to fast while traveling if no hardship imposed. in any case, travelers should make up the days they missed out in ramadan once ramadan is over and they are back home.

as for those whose sickness does not allow them to fast, they fall into three categories:

 if it is neither hard nor harmful for them, they must observe fasting.

 if it is hard but not harmful for them, they are permitted to break their fast.

 if it is harmful for them, then they must abstain from fasting. it is stated in the quran:

 "do not kill yourselves" and "do not throw yourselves into destruction."  [noble quran 2:195]

the prophet (peace be upon him) is reported to have said: "cause no harm to yourselves nor cause it to others."

[from the collection of sayings of the prophet (peace be upon him) collected by imam muslim]

the days that happen to be missed in ramadan must be made up once ramadan is over.

during the monthly menstruation of women or postnatal time after giving birth, women should not fast, but they must make up these days that are missed as soon as possible in the following month(s). pregnant or breastfeeding women whose health or the baby's health would be negatively affected by the fasting should break their fast and then make them up in the future as soon as it is not a problem for their health.

it is also recommended for those engaged in combat in the way of allah to break their fast. the prophet (peace be upon him) told his companions in one of the battles: "you are going to meet your enemy in the morning, abstaining from fasting is better for your strength, so break your fast."

[from the collection of sayings of the prophet (peace be upon him) collected by imam muslim]