There are five activities that are prohibited on Yom Kippur: eating (and drinking), wearing shoes, anointing, washing, and marital relations. This article will focus on the prohibitions of wearing leather shoes, anointing and washing.

Which Prohibitions are Biblical in Nature?
The Gemara, Yoma 76a-77b, notes that all five prohibited activities are considered inui (self-affliction, based on the verse "ve'initem et nafshoteichem," you shall afflict yourselves, mentioned by the Torah four times in reference to Yom Kippur). The Gemara then brings a source from Tanach that each of these activities are considered a form of inui.

The implication of the Gemara is that the biblical commandment of inui includes all of these prohibited activities. This in fact is the opinion of R. Eliezer of Metz, Sefer Yerei'im no. 420. Rabbeinu Tam (cited in Tosafot Yoma 77a, s.v. D'T'nan) notes that there are a number of leniencies mentioned by the Mishna and the Gemara regarding the prohibitions other than eating and drinking. Leniencies of this nature are generally indicative of the fact that the prohibition itself is only rabbinic in nature. For this reason, Rabbeinu Tam concludes that while eating (and drinking) on Yom Kippur constitutes a biblical violation, the other prohibitions of washing, marital relations, anointing, and wearing shoes are only prohibited by rabbinic law.

Ran, Yoma 1a, s.v. Yom, notes Rabbeinu Tam's position that only eating and drinking are biblically prohibited. However, he is not willing to ignore the implication of the Gemara that all five forms of inui are biblically mandated. Therefore, Ran suggests that the requirement of inui only specifically includes eating and drinking. The Torah then left it to the rabbis to interpret which other activities are included in inui. The rabbis, based on verses in Tanach, chose wearing leather shoes, anointing, washing, and marital relations as activities that are part of the biblical prohibition of inui, but in choosing these four activities, they applied certain leniencies. This is why the Gemara implies that the prohibitions are of a biblical nature, while the leniencies associated with them seem to indicate that the prohibitions are rabbinic in nature.

The Prohibition of Washing
The Gemara, Pesachim 54b, states that the prohibition of washing on Yom Kippur applies to washing any part of the body. Even washing one's finger is prohibited! However, the Gemara, Yoma 77b, lists numerous leniencies associated with the prohibition of washing on Yom Kippur: It is permissible to wash one's hands if they are dirty; it is permissible to rinse one's hands before feeding a child; it is permissible to wade across a river in order to greet one's rabbi; and it is permissible to wade across a river in order to guard one's property. Tosafot, op. cit., explain that the prohibition of washing on Yom Kippur is limited to washing that is for the purpose of enjoyment. If one washes for any reason other than enjoyment, there is no prohibition. [R. Avraham Borenstein, Avnei Nezer, Orach Chaim no. 182, adds that although one does receive pleasure by washing one's hands or body for non-enjoyment purposes, the prohibition only applies if one actually intends to receive pleasure and not if it is an incidental result.]

Rabbeinu Tam, (cited in Tosafot, Yoma 77b, s.v. Mishum) states that it is permissible to wash one's hands for netilat yadayim in the morning because washing hands to remove ru'ach ra'ah (ritual impurities that reside on the hands) is no different than washing hands to remove dirt. Rambam, Hilchot Tefillah 7:8, rules that on Yom Kippur, one does not wash his hands in the morning and one does not recite the beracha of Al Netilat Yadayim. Shulchan Aruch, Orach Chaim 613:2, codifies the opinion of Rabbeinu Tam. He adds (based on the comments of Rabbeinu Yerucham 7:2) that one should only wash the fingers, not the whole hand. This is because washing one's fingers is sufficient to remove the ru'ach ra'ah (see Magen Avraham 4:7). [Perhaps Rambam is simply following his own opinion that ru'ach ra'ah no longer exists (see Yabia Omer, Yoreh Deah 1:9, for a lengthy discussion on the existence of ru'ach ra'ah nowadays). Rambam, Hilchot Tefillah 4:1-2, is clearly of the opinion that the reason why one performs netilat yadayim in the morning is to remove dirt from one's hands. Rambam states that if there is no water available, one can simply wipe one's hands clean. Apparently, Rambam is of the opinion that the permission to wash one's hands if they are dirty only applies if there is no way to clean the dirt without water. Rambam implies this position elsewhere; see Hilchot Shevitat Asor 3:3.]

The Prohibition of Anointing
Tosafot, op. cit., note that just as washing is only prohibited if done for enjoyment purposes, so too, anointing is only prohibited if it is done for enjoyment purposes. Ran, Yoma 1b, s.v. V'Im, disagrees and maintains that anointing is prohibited even if it is not for enjoyment purposes. Rambam, Hilchot Shevitat Asor 3:9 also prohibits anointing for non-enjoyment purposes.

The dispute between Tosafot and Ran (and Rambam) seems to be contingent on the source for the prohibition of anointing. The Gemara, Yoma 76b, provides two reasons for the prohibition of anointing. First, it is a form of inui. Second, anointing something on one's body is tantamount to drinking it and therefore, anointing can be viewed as a lesser form of drinking.

Tosafot, Yoma 77a, s.v. Minayin, note that the two reasons complement each other. There are many forms of inui that are permitted on Yom Kippur, such that simply defining anointing as inui would not necessarily be sufficient to prohibit it on Yom Kippur. Similarly, Tosafot assert that the principle that anointing is tantamount to drinking is not applied to all areas of Halacha, such that this reason alone might not be sufficient to prohibit anointing on Yom Kippur. In combination though, these two reasons combine and complement one another to prohibit anointing on Yom Kippur. Tosafot then write that one does not apply the principle that anointing is tantamount to drinking if there is no inui involved and this is the reason why anointing is permissible if it is not for enjoyment purposes. Based on the comments of Tosafot, Sha'ar HaMelech, Hilchot Shevitat Asor 1:5, suggests that Rambam (Ran) is of the opinion that the prohibition of anointing is a direct function of the principle that anointing is tantamount to drinking. Accordingly, there is no distinction between anointing for enjoyment purposes and anointing for other purposes just as there is no such distinction regarding drinking. [See also Harerei Kedem 1:50.]

The Prohibition of Wearing Shoes
The Gemara, Yoma 88b, states that one is permitted to wear shoes on Yom Kippur if his intention is to protect himself from being bitten by a scorpion. Maharil, Hilchot Leil Yom Kippur, no. 2, implies that anyone who has difficulty walking barefoot is technically permitted to wear shoes. This ruling is codified by Rama, Orach Chaim 614:4. It is implicit from Maharil's ruling that the prohibition of wearing shoes is similar to the prohibition of washing in that the prohibition only applies if one is wearing the shoes for the purposes of comfort, not utility.

The Gemara, Yoma 88b, queries whether the prohibition of wearing shoes on Yom Kippur applies to all shoes or whether it is limited to leather shoes. According to Rif, Yoma 2a, the conclusion of the Gemara is that it is permissible to wear non-leather shoes. According to R. Zerachia HaLevi, Ba'al HaMa'or ad loc., it is prohibited. Rambam, Hilchot Shevitat Asor 3:7, implies that non-leather shoes are permitted only if they are soft enough so that one feels as if he is barefoot.

Shulchan Aruch, Orach Chaim 614:2 rules in accordance with the opinion of Rif that it is permissible to wear non-leather shoes. Mishna Berurah 614:5, writes that if possible, it is preferable to be stringent on the matter. The practical method he suggests (for those who wish to follow the stringency) is to wear the non-leather shoes to walk from place to place (as per the leniency of Maharil) and then to remove the shoes while indoors. [Maharil himself, in allowing one to wear leather shoes outdoors (if he has difficulty walking barefoot), only permits doing so if one does not have non-leather shoes.]