Standing for an old person:
The age defined as elderly: An elderly person is defined, in this regard, as a person who has reached 70 years of age. [According to the Arizal and Kabala, one is to stand for a person who has reached 60 years of age.]
Standing for an elderly ignoramus/Rasha: The above obligation to stand before the elderly applies even if the old man is an ignoramus, so long as he is not a Rasha. [One who does not wear Tefillin, or Daven, is considered a Rasha, and one is not obligated to stand in his honor. It is unclear if this applies even in a case that the person is a Tinok Shenishbah.]
Standing for a gentile elder: [One is not required to stand in honor of an elderly gentile, however] one is to honor and respect him with words, and give him a hand of support.
A Sage standing for an elder: Even a young Sage must stand for an elderly man who is very old. [If, however, he is a greater Sage than the elderly man] he is not required to fully stand, and it suffices to slightly [get up to] show him honor.
An elderly man standing for another elder: An elderly man is not required to stand for another elderly man, and it rather suffices to simply show some form of respect.
Must one stand for an elderly woman?
 Implication of Rav Issi Bar Yehuda in Kiddushin 32a who includes a Zakein Ashmaiy in the verse and Rashi ibid states “The word Seiva in the verse implies every old man”; Implication of Minyan Hamitzvos of Rasag; Implication of Beis Yosef 244 who brings Rashi ibid; Implication of Minchas Chinuch Mitzvah 257; See Chinuch Mitzvah 257 who only adds “standing for elders” later on in the Mitzvah and Minchas Chinuch ibid questions if the Chinuch learns it is part of the Biblical Mitzvah or not, nonetheless, he concludes that we rule like Rav Isi Bar Yehuda; See however Rambam Mitzvah 209 who makes no mention at all that it is included in the Biblical command, and likewise in Hilchos Talmud Torah 6:9 he does not write it as a command at all, and simply states that “One is to stand for him.” This strongly implies that he does not learn this to be a Biblical command. Likewise, the Michaber ibid and Tur ibid writes standing for elders only in the end of the Halacha, and states “Likewise it is a Mitzvah.” It is unclear if the intent of the Michaber/Tur is to state that it is likewise a positive command, or if his intent is to say that it is a Mitzvah, but not a positive command. See Sefer Hamitzvos Rasag of Rav Perlow Mitzvah 11-12. Vetzaruch Iyun.
 Michaber ibid; Tur 244; Rambam Talmud Torah 6:9; Chinuch Mitzvah 257; Semag 13; Rebbe Isi Ben Yehuda in Kiddushin 32b; Rebbe Yochanon in Kiddushin 33a that the Halacha is like Isi
The reason: As the verse in Parshas Kedoshim [Vayikra 19:32] states “Mipnei Seiva Takum”, which means that one is to get up for his elders.
Other opinions: Some rule there is no obligation to stand for an elder who is not a Torah scholar. [Tana Kama and Rebbe Yossi Hagelili in Kiddushin ibid; Pesikta on Parshas Kedoshim omits opinion of Issi ben Yehuda; Implication of Sheilasos on Kedoshim ibid; Implication of Rashi Kedoshim ibid; Implication of Or Zarua, Yireim, Ravaan p. 137 who omit the words “Elder”; See Sefer Hamitzvos Rasag of Rav Perlow ibid]
 Michaber ibid
 Brought in Birkeiy Yosef 244; Ben Ish Chaiy Ki Seitzei 2:12; Minchas Chinuch 257
 Rama ibid; Beis Yosef in name of Tosafos Kiddushin 32; Hagahos Maimanis 6; Mordechai; Rabbeinu Yerucham; Ran; Rabbeinu Tam
 Ben Ish Chaiy Ki Seitzei 2:12
 Michaber 244:7; Kiddushin 33a
 Michaber 244:7
 Shach 244:5
 Michaber 244:8
 Sefer Chassidim 578; Beis Yehuda Y.D. 1:28; Minchas Chinuch 257:3 based on final ruling like Rebbe Issi Bar Yehuda; Kiryat Chana David 1:15; Yechaveh Daas 3:72; Implication of Chinuch ibid, and all other Rishonim who record “This Mitzvah applies to both men and women”
 Halachos Ketanos 1:154; Ben Ish Chaiy Ki Seitzei 2:16; Rav Poalim 2 Kuntrus Sod Yesharim 9 based on Arizal in Shaar Hamitzvos Kedoshim; Shevet Halevi 1:114; See Avnei Yashpei 1:188