Gemara

We know the direct benefit of Tefilin - "all the nations will see that Hash-m's name is called upon you";

(Beraisa - R. Eliezer ha'Gadol): This refers to the Tefilin Shel Rosh (of the head).

Menachos 35b (Rav Chana bar Bizna): "V'Hasirosi Es Kapi v'Ra'isa Es Achorai" - Hash-m allowed Moshe to see the knot of His Tefilin.

37b (Beraisa): "Al Yadecha" refers to the upper arm.

Suggestion: Perhaps it refers to the palm!

Rejection (R. Eliezer): We learn from "v'Hayah Lecha l'Os" - it is a sign to you (the wearer), not to others (for it is covered by clothing).

Ameimar had a wound. His shirt was torn (to avoid aggravating the wound). His Tefilin could be seen through it.

Rav Ashi: Don't you agree that "v'Hayah Lecha l'Os" teaches that it must be visible to you, but not to others?!

Ameimar: No. The verse teaches that Tefilin Shel Yad (of the hand) is worn in a place on the arm normally covered (not the palm).

Erchin 3b: One might have thought that Kohanim are exempt from Tefilin;

"U'Keshartam l'Os Al Yadecha v'Hayu l'Totafos Bein Einecha" teaches that the Mitzvah to wear Tefilin Shel Rosh applies only to those commanded to wear the Shel Yad. Kohanim do not wear the Shel Yad (during Avodah), for it would interrupt between their skin and Bigdei Kehunah, which must be "Al Besaro." Therefore, a Beraisa needed to teach that they are obligated. This is because neither Tefilin is Me'akev the other.

Question: Why do they wear head Tefilin? "V'Samta ha'Mitznefes Al Rosho" requires the turban to be on his head without an interruption!

Answer (Beraisa): The Kohen Gadol's hair was visible between the Mitznefes and the Tzitz. He would wear Tefilin there.

Megilah 24b (Mishnah): Outsiders put Tefilin on the sleeve.

Rishonim

Rif and Rosh (Hilchos Tefilin (after Menachos) 8a,9a and Simanim 12,18) bring the Gemara in Sotah and in Menachos.

Rosh (12): "All the nations will see..." refers to the Tefilin Shel Rosh, for it is more visible than the Shel Yad, about which it says "it is a sign for you."

Rosh (18): The Gemara in Erchin teaches that Tefilin must be on the skin. One may not wear them on the Mitznefes.

Ran (Megilah 15b DH v'Nosnah): Outsiders put Tefilin on the sleeve to fulfill "it will be a sign." They do not expound "it is a sign to you", but not to others. The Rashba infers that the Shel Rosh, which should be exposed, may be on top of clothing. The Kohen Gadol wore Tefilin between the Mitznefes and the Tzitz. Perhaps another Kli of a Mitzvah may not be on top of the Mitznefes.

Mordechai (Hilchos Tefilin p.12a): Shimusha Rabah says that Tefilin must be covered, for it says "Lecha l'Os." R. Tzemach says that "v'Ra'u (all the nations will see...)" refers to the Shel Rosh, which is exposed on the head. The Shel Yad is under his garment - "it is a sign for you." Also, there is a Shin on the Shel Rosh; the Yud and Dalet on the Shel Yad are not mentioned anywhere. Surely, it is good that the Shel Rosh be exposed, for it says "the nations will see", and Moshe was allowed to see "Achorai", i.e. the knot of Hash-m's Tefilin. We can say that Shimusha Rabah agrees that the knot must be exposed. However, nowadays we are concerned and cover it, even though it is improper.

Note: Hagahos Mahari and Machatzis ha'Shekel say that the text should say 'we are not concerned, and cover it. The Beis Yosef's (OC Sof 27) text said 'we are concerned for haughtiness, and cover it.'

Beis Yosef (DH Kasuv): Sefer ha'Terumos (211) says that Shimusha Rabah refers only to the Shel Yad. Orchos Chayim (Hilchos Tefilin 17) says that the Shel Yad must be covered due to "Lecha l'Os", and the Shel Rosh must be exposed due to "v'Ra'u".

Poskim

Shulchan Aruch (OC 27:5): If one is prone to get sick from the cold if he exposes his head, and cannot put Tefilin directly on his head, he can put it on a thin cap, and cover it lest people see (that his Tefilin is on his skin).

Beis Yosef (DH veha'Rivash): This is better than not wearing Tefilin at all.

Sha'arei Teshuvah (6/8): Tashbatz (30) allows covering the Shel Rosh, but not to put it on a garment. "V'Ra'u..." only teaches where we put on Tefilin. It does not mean 'they will see', rather, they will hear, like "Ro'im Es ha'Kolos."

Shulchan Aruch (11): It is good for the Shel Rosh to be exposed.

Mishnah Berurah (45): It is good that also the knot be exposed. However, this is not the custom.

Magen Avraham (8:3): The Ari Zal would cover the Shel Rosh with the Talis. However, one should not totally cover it; see Siman 27.

Machatzis ha'Shekel: It must be exposed, due to "v'Ra'u..." The Talis should be a roof over the Shel Rosh, but the Shel Rosh can be seen from the front.

Kaf ha'Chayim (8:11): The Magen Avraham means that one should not cover it the entire day, but during Tefilah it should be totally covered; it bulges and it is evident from the outside. The Magen Avraham (below, 20) says that even when the Shel Rosh is covered, it is evident that he is wearing Tefilin.

Shulchan Aruch (ibid.): However, it is improper for a Talmid to expose his Tefilin in front of his Rebbi.

Rav Hai Gaon (cited in Beis Yosef Sof ha'Siman): This is improper, for Tefilin are a matter of honor. One should not equate himself to his Rebbi.

Magen Avraham (20): A Talmid can remove his Rebbi's shoe without concern lest people say that the Talmid is a slave, for it is evident that he is wearing Tefilin. Even though the Tefilin is covered, it sticks out in the hat.

Rema: We are not concerned whether the Shel Yad is covered or exposed.

Mishnah Berurah (47): in any case it is better that it be covered.

Sha'arei Teshuvah (11) and Kaf ha'Chayim (25:32): Some are meticulous to drape the Talis over it while putting it on the arm. The Ari Zal says that it should be put on covertly.

Rema (ibid.): It seems that nowadays that we wear Tefilin only at the time of Kri'as Shema and Tefilah, even a Talmid in front of his Rebbi can reveal even the Shel Rosh. The custom is not to be careful about this.

Magen Avraham (21): We are not concerned if the sleeve is torn and the Shel Yad is visible, but the Tefilin may not be on top of the sleeve.