Gemara

(R. Akiva): When afflictions are sent on a person, they must accept an oath only to leave at a particular time, through a particular doctor, and through a particular medicine.

(R. Yochanan): "Va'Chalayim Ra'im v'Ne'emanim" - the sicknesses fulfill a mission to do evil. They are trustworthy to fulfill their oath.

Bava Kama 85a (Beraisa - Tana d'Vei R. Yishmael): "V'Rapo Yerapei" permits doctors to heal.

Berachos 60a (Rav Acha): One who goes to let blood prays "may this be for a cure. May You heal me, for You are a faithful healer. Your cure is a true cure". It is improper for people to engage in Refu'ah, but they accustomed themselves to.

Objection (Abaye - Beraisa): The Torah permits doctors to heal!

After letting blood, he blesses "the One who heals for free."

Medrash Shmuel (4:1): R. Yishmael, R. Akiva and a farmer (Ploni) were walking. They encountered a Choleh. R. Yishmael and R. Akiva told him how he can be cured.

Ploni: Hash-m made him sick. Why do you get involved?!

R. Yishmael and R. Akiva: Hash-m made the field. Why do you get involved in His matter and eat His fruits?!

Ploni: If I would not plow, cover, fertilize and weed, nothing would grow.

R. Yishmael and R. Akiva: Fool! "Man's days are like grass." If one does not fertilize, weed and plow, a tree will not sprout. If it sprouts and it does not drink water, it will die. Man is the same! The medicine is the fertilizer, and the doctor is the farmer.

Rishonim

Rambam (Hilchos De'os 4:23): A Chacham may not live in a city without a doctor (and) bloodletter.

Rosh (Nedarim 4:8): Refu'ah is a Mitzvah. The Yerushalmi says that a Choleh does not merit to be cured by everyone.

Ibn Ezra (Shmos 23:25): One who observes the Torah has no need for doctors along with Hash-m. Therefore, it says "in his (Asa's) sickness he did not seek Hash-m, rather, doctors."

Ramban (Vayikra 26:11): A Chasid who observes all the Mitzvos, Hash-m will guard him from every sickness, sterility and miscarriage, and fulfill his days with goodness. If Yisrael will be totally righteous, Hash-m will not act with them according to nature. He will remove sickness, and they will not need doctors - "Ani Hash-m Rof'echa." At the time when there was prophecy, Tzadikim (e.g. Chizkiyah ha'Melech) would not seek doctors when calamity befell them, rather, prophets. Divrei ha'Yomim (2:16:12) criticizes Asa for seeking doctors, and not prophets. This shows that it was not normal to seek doctors. Doctors are merely to tell us which foods are healthy to eat (but not to remove sickness). The 22 years that Rabah was Rosh Yeshiva, Rav Yosef (who should have been Rosh Yeshiva, but pardoned this to Rabah) did not need to call even a bloodletter to his house (Berachos 64a). The Medrash says that a gate that is not open to Mitzvos is open to doctors. People should not need doctors. A person would get sick based on his Aveiros, and get healed when Hash-m desires. People accustomed themselves to doctors, so Hash-m left them to nature (Berachos 60a). Chachamim expounded that a doctor may heal. They did not expound that a Choleh may get healed (through medicine), for this is merely the custom of people not from Hash-m's congregation. If a doctor is expert, we do not forbid him to heal lest he err, or so people will know that Hash-m alone heals. One who wounded another must pay for Refu'ah; the Torah does not rely on miracles. However, one who does Hash-m's will has no involvement with doctors.

Beis Yosef (YD 336 DH u'Mah she'Chosav she'Lo): it is merely their custom. It is Reshus, i.e. a Mitzvah to heal.

Perush ha'Mishnayos (Pesachim 4:10): Sefer Refu'os was a list of cures that should not heal (like some say that 'Talsam' in a certain order heals particular illnesses), and other forbidden things. The author wrote it to be an academic treatise about nature, but not for people to use it. "Do not learn to do", but you may learn to understand and give Halachic rulings. Perhaps the Sefer discussed combinations of ingredients that cause certain illnesses, and how to cure them, so when a doctor sees it he will know the cause and the cure. People degenerated and used it to kill people, therefore, Chizkiyah put it in Genizah. Some say that Shlomo composed it so that a Choleh could learn from it how to be cured. Chizkiyah saw that people were not trusting in Hash-m, rather, on the Sefer, so he hid it. This is folly. The Gemara says that Chachamim agreed to this! If a person is hungry, and he eats bread, he will surely be cured from his pain. Did he remove his trust from Hash-m?! Tell the fools 'just like I thank Hash-m when I eat, that He gave me (food) to remove my hunger, so one thanks Him for giving a Refu'ah to remove the illness!'

Rashba (1:414): I am astounded that such a clear mind (the Rambam) erred so greatly about Genizah of Sefer Refu'os. Chizkiyah burned the copper snake that Moshe made, but he only buried Sefer Refu'os!

Yad Chanoch (49, Hagahah): The Rambam's source is a Beraisa in Medrash Temurah and Medrash Shmuel. R. Akiva proved that engaging in Refu'ah is not removing one's trust from Hash-m. The Ramban's and Rashba's difficulties are with the Medrash, not with the Rambam!

Note: The Ramban and Rashba hold that it was not hidden (for 300 years) until the days of Chizkiyah, for then people began relying solely on the Sefer and not on Hash-m, even though prophets were around. Perhaps other cures do not work as quickly, so this is not a concern. Alternatively, after the Churban there is so much Hester Panim (Hash-m is so hidden) and people are so used to doctors that we do not discourage the masses from seeking doctors.

Poskim

Shulchan Aruch (YD 336:1): The Torah permits doctors to heal. It is a Mitzvah. It is part of Piku'ach Nefesh.

Taz (1): True Refu'ah is through asking mercy from Hash-m - 'I struck, and I heal." However, not all merit this, so one must engage in 'natural' cures. Hash-m consented, and gave Refu'ah through nature. This is the Torah's Reshus. Rav Acha holds that one must apologize for seeking natural Refu'ah, like the custom of people, and acknowledge that true Refu'ah is from Hash-m. Abaye disagrees, for the Torah consented.

Yad Avraham: It is permitted only if he knows that his Refu'ah is from Hash-m, and does not depend on the medicine or the doctor.

Degel Machaneh Efrayim (Likutim DH b'Zohar): The Zohar (and Bava Basra 58b) say that people need medicines only where there is no wine. One who has complete trust in Hash-m needs no doctor. "V'Rapo Yerapei" permits doctors to heal; not everyone needs this. 'Wine' alludes to Hash-m - "Chikech k'Yayin ha'Tov." Or, it alludes to Torah, which is expounded in 70 ways, like the Gematriya of Yayin.

Shulchan Aruch (OC 230:4): One who goes to let blood prays "may this be for a cure. May You heal me, for You are a faithful healer. Your cure is a true cure". It is improper for people to engage in Refu'ah, but they accustomed themselves to. After letting blood, he blesses "the One who heals for free."

Mishnah Berurah (6): One says the same for any Refu'ah. He should realize that the Refu'ah comes only from Hash-m. Through the Tefilah, he trusts in Hash-m and requests that He cause it to heal.

Mishnah Berurah (7): The Beis Yosef says that one blesses with Shem and Malchus, but this is not the custom.

Gra (2): The text of Bahag, Rambam, and Tur is 'blesses is He who heals the sick.

Igros Moshe (YD 4:8:1): The Torah gave permission to heal. The Rambam and most Rishonim hold that it is a Chiyuv.

Tzitz Eliezer (5 Ramat Rachel 1): The Aruch ha'Shulchan (230:5) says that one may not rely on doctors alone. He should be clearer, that one must rely only on Hash-m. The doctor and medicine are Shluchim that Hash-m prepared beforehand, like it says in Avodah Zarah. Chovas ha'Levavos (Sha'ar ha'Bitachon 3) says that Asa's mistake was to also rely on doctors. One could explain the Chovas ha'Levavos like the Ramban, that Asa should not have sought doctors at all, but it seems that he holds that the only mistake was relying also on them. The Ibn Ezra holds that based on Asa's great righteouness, it was a blemish in his trust in Hash-m to seek doctors. The Rambam admits that one must rely only on Hash-m, also while engaging in the cure. Seeking doctors must be like planting seeds, with reliance on Hash-m; perhaps this is the time and the man through whom the illness will go away.