The Rabbis instituted certain practices to remind oneself of the destruction of the temples.
==Seeing the Kotel nowadays==
# One who sees the Kotel in it’s destruction should rip his shirt a tefach and not have it sown up. <Ref> S”A O”C 561:2 writes that when one sees the place where the Mikdash used to stand and now remains in it’s destruction, one must rip one’s shirt a Tefach. Even though Sh”t Bet Mordechai 33 is lenient not to rip one’s shirt nowadays since Har HaBayit is under Israeli control, almost all achronim including Rav Ovadyah in Chazon Ovadyah (Vol. Arba Taniot pg 438), Rav Moshe Feinstein in Sh”t Igrot Moshe O”C 4:70:11, Rav Vosner in Sh”t Shevet HaLevi 7:78, Rav Hadayah in Sh”t Yaskil Avdi 8:25:4(4), and Zichron Betzalel pg 143 agree that even though Har HaBayit is in Israeli control, it’s still an obligation to rip one’s shirt upon seeing the Makom HaMikdash. Moadim UZmanim (Vol 7 pg 209-11) writes that the Minhag not to rip one’s shirt can rely on those who say that really the ground that the Bet Hamikdash once stood and not the Kotel which is just a wall of Har HaBayit. (so writes Rav Tukachinsky in Eretz Yisrael 22:5). Another leniency which isn’t LeHalacha but just to defend the minhag is nowadays we don’t feel the churban like those who live in Yerushalyim unless it’s our first time or it’s been 12 months. Sh”t Mishnat Halachot 6:110 defends the minhag similarly by saying that in our sorry state a person would feel worse for the loss of his shirt than for the loss of the churban, however, someone who feels for the loss of the Churban should rip the shirt and fulfill the Halacha. </ref>