Women:[1]

Women are exempt from wearing Tefillin.[2] Furthermore, they are to be protested against doing so.[3]

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[1] 38/3; Michaber 38/3; Mishneh Brachos 20

Male slaves: Male slaves follow the same law as women and are exempt from Tefillin. [Admur ibid]

[2] The reason: As Tefillin is a time dependent positive command [Admur ibid; Michaber ibid], as Shabbos and Yom Tov is not a time for Tefillin. [Admur ibid; Taz 38/1] However nighttime is a time that one is Biblically obligated in Tefillin. [Levushei Serud ibid] The Yerushalmi Brachos 3/3 explains that women are exempt from Tefillin due to that Tefillin is connected to Torah learning in the verse, and hence just like women are exempt from learning Torah, similarly they are exempt from Tefillin. Vetzaruch Iyun from Admur 17/1 in which he explains that the reason women are exempt from Tefillin is not due to that it is a time dependent Mitzvah, but due to other reasons [seemiongly the reason of the Yerushalmi]. Hence, why does Admur 38/3 not record this ruling of the Yerushalmi. Vetzaruch Iyun. See letter of Rebbe printed in Haggada Shel Pesach p. 620.

According to Kabala: According to Kabala the Mitzvah of Tefillin only applies to men, while women are not relevant to this Mitzvah. [Arizal brought in Shaar Hakavanos 5; Kaf Hachaim 38/8]

[3] Admur ibid; Rama 38/3; Maharam; Kol Bo 21; Birkei Yosef 38/1

The reason: If women decide to be stringent upon themselves to wear Tefillin they are to be protested [despite the fact that they may do Mitzvos that they are exempt from] being that they do not know to guard their bodies in the cleanliness [required for Tefillin]. [Admur ibid; Taz 38/2; M”A 38/3; See Olas Tamid 38/4; Tehila Ledavid 38/1]

Other opinions-Biblical prohibition: Some Poskim rule that it is Biblically forbidden for women to wear Tefillin due to the prohibition of Lo Silbash. [Beis Hillel 182/2; Targum Yonason Seitzei; Kaf Hachaim 38/9]

Michal Bas Shaul: Michal the daughter of Shaul wore Tefillin without protest. [Eiruvin 96] ] Some suggest this was due to that Michal knew that she had soul of a male, as we see from the fact she could not have any children, and hence based on Kabala the Mitzvah of Tefillin was relevant to her. [Yifei Lalev 38/2; Shomer Emuinim Ki Seitzei; Kaf Hachaim 38/9]

The daughters of Rashi: There is no known source for the common conception that Rashi’s daughters wore Tefillin.