Men shaving armpit and pubic hair:
It is forbidden for a man to remove his armpit hair or his pubic hair. This applies even against using scissors to shave the hair to a razor like cut [i.e. Keiyn Taar]. [One who transgresses the above has transgressed a Rabbinical command.] In previous times, one who shaved the above areas would have been liable for receiving Rabbinical lashes [i.e. Makas Mardus].
Areas that men also shave: The above prohibition only applies in an area that only women shave their armpits and pubic area. However in an area which is common also for men to shave the above places of the body, then one who shaves it does not receive Rabbinical lashes. Furthermore, in such communities a man may even initially shave these areas of the body. Nevertheless, the scrupulous Jews [i.e. Chaveirim] avoid shaving these areas of the body even in such communities. [Likewise, according to Kabala, one is to abstain from doing so.]
Areas that women do not shave: If a man shaved his pubic hair in a community that even women do not shave their pubic hair then he is not liable for lashes [although a Rabbinical prohibition remains].
Itching the armpit and pubic area: It is forbidden to itch with one’s hands the hair of one’s armpit and pubic area with intent to remove the hair. It is however permitted to itch it using his clothing.
Shaving for medical purposes: [It is permitted to shave the armpit and pubic hair for medical purposes. Thus] one who has a painful skin ailment in his armpit or pubic area, and the pain is being aggravated due to the hair, may shave off the hair.
May a man trim armpit and pubic hair?
In judging the common practice of men in an area vis a vis pubic shaving, does one follow the gentile or Jewish custom of men?
May one pluck out pubic hair with his finger?
Women growing pubic hair:
 Michaber 182/1; See Tzemach Tzedek Y.D. 93
 The reason: This is forbidden due to the prohibition against Lo Yilbash, that a man may not dress like a woman. The Sages expounded that this verse includes not only a prohibition against wearing actual clothing of a woman but towards doing any action done to the body by women for beauty purposes.
 Michaber ibid; Bahag; Tosafus Nazir 59b; Rosh; Rif
Other opinions: Some Poskim rule it is permitted to use a scissor to shave the armpit and pubic hair to even a razor like shave. [Rabbeinu Tam, brought in Tzemach Tzedek ibid]
 Taz 182/6
The reason: Removing the hair of the body does not contain a Biblical transgression of Lo Silbash being that the Biblical transgression only applies to actions that visibly make the person appear like the opposite gender, and thus since removal of private hair is not visible to others it does not fall under the Biblical prohibition. [Taz ibid]
Other opinions: Some Poskim rule it is a Biblical prohibition to shave the armpit and pubic hair using a razor. [Rav in Nazir 58b as explained in Tzemach Tzedek ibid; Semak 33; Conclusion of Tzemach Tzedek 93/4]
 Michaber ibid; Tur; Rambam
 Michaber ibid
The reason: As the entire reason for the prohibition is so one not enhance his body similar to that of a woman. [Michaber ibid]
 Rama ibid; Ran Avoda Zara
 Rama ibid; Ran ibid; Nimukei Yosef
 Torah Leshma 215 based on Arizal in Shaar Hamitzvos Parshas Kedoshim
The reason: As just as above there is a higher beard with the 13 Tikkunei Dikna, the same applies below by the lower beard. [Arizal ibid]
 Taz 182/5
 Michaber 182/2
 Shach 182/4; Perisha 182; Tzemach Tzedek Y.D. 93-1
 Tur in name of Geonim; Tosafus and Rosh Yevamos
 The reason: As it is clearly evident that such a shave is not done for beauty purposes. Furthermore, even if the man intends to do so for beauty purposes, since in truth it does not beautify him but rather makes a mockery of him, therefore we ignore his intents. [Sahch 182/5]
 Michaber 182/3; Nazir 59a
 Michaber 182/4; Rashba
 Shach 182/5
 Michaber 182/1 that only a razor like shave is forbidden and not a trim; Beis Yosef 182; Kitzur SHU”A 171/2; Torah Leshma [of Ben Ish Chaiy] 215 [However perhaps he refers only to an area that also men shave]
 Rashba 1/106; Tzemach Tzedek Y.D. 93 “If the Beis Yosef would have seen the ruling of the Rashab ibid certainly he would have ruled this way”; Semak 33 writes a Baal Nefehs is to be stringent
 Perisha 182, brought in Rav Akiva Eiger 182
 Igros Kodesh 6/268, [printed in Shulchan Menachem 4/133]
 Torah Leshma [of Ben Ish Chaiy] 215
 Sanhedrin 21a
 2nd explanation in Ran ibid; Torah Leshma [of Ben Ish Chaiy] 215
 1st explanation in Ran ibid; Mahrshal
 Rashi ibid
 See Torah Leshma ibid