The widespread Orthodox practice is for women not to don tefillin or wear a tallit with tzitzit while praying.
Following the controversial arrests of a non-Orthodox woman who prayed at the Western Wall while wearing these articles, it behooves us to understand the underlying dispute within Jewish law.
As a general principle, talmudic law exempts women from performing timebound positive commandments, such as blowing a shofar on Rosh Hashana or dwelling in a succa (Kiddushin 29). The Talmud derives this principle from the commandment of tefillin, which are deemed 'time-bound' since they are not worn on Shabbat or holidays (33b). Some explain that this is a pragmatic exemption which removes time pressure from women already consumed with household duties (Avudraham, Sha’ar 3), while others contend that women have superior inherent spiritual wisdom (bina) and do not require timely religious imperatives (Rabbi S.R. Hirsch, Leviticus 23:43). Be that as it may, the Talmud notes that there are many exceptions to this rule, with women remaining obligated in many time-bound commandments such as Shabbat and Pessah rituals."
