Techelet

• The pesukim in Shalach introduce the mitzvah of Tzitzit and among them is one that mentions the requirement to have a string of the Techelet color.

"דבר אל בני ישראל ואמרת אלהם ועשו להם ציצת על כנפי בגדיהם לדרתם ונתנו על ציצת הכנף פתיל תכלת"

• The Mishna (menachot 38a) writes clearly that wearing Tzitzit without Techelet also fulfills the mitzvah of Tzitzit (while lacking a part of the mitzvah). This is codified in the Rambam (Tzitzit 1:3).
• From the end of the era of the sages of the Gemara Techelet became unavailable and extinct from common practice. However, in the last century and a half many have investigated this lost dye and some claim to have rediscovered it. The halachic question is how to deal with the dyes which some have claimed to be the real Techelet of the Torah.
• Rav Hershel Schachter in Ginat Egoz (Siman 2) writes that there is very little reason not to wear the Tzitzit because of a doubt that perhaps it is the correct Techelet. He addresses the fact that the minhag is to wear a white garment with white strings, but says clearly that there’s no reason that this minhag should override a possibility to fulfill a biblical mitzvah. Furthermore, the Bet HaLevi (Sh”t Bet HaLevi 42) who says that there’s a prohibition of detracting from the מצות by fulfilling a mitzvah in a inferior way but that since a positive mitzvah overrides a negative one, there’s still reason to wear Tzitzit without Techelet because one still fulfills a positive mitzvah. Extending this further, Rav Schachter writes that if a person owns Techelet then it becomes possible to fulfill the positive mitzvah and negative one simultaneously and therefore one wouldn’t be allowed to use a positive mitzvah to override a negative one. To see how Rav Schachter ties the Techelet Tzitzit see here www.tekhelet.com.
• There are other Poskim who hold of wearing Techelet but most don't hold it is as much as a Chiyuv as Rav Schachter. Rav Meir Mazuz, Rosh Yeshiva of Kiseh Rachamim in Bnei Brak, wears Techeles on Shabbos as he holds it's not a Chiyuv rather a nice Chumra.
• However, the overwhelming minhag for the last century was not to wear the Techelet which were suggested as the real species of Techelet. There’s a short article of Rav Elyashiv (Kovetz Teshuvot 1:2) who mentions several reasons to defend this practice. See Teshuvot vihanhagot 1:29 and 4:5 who quotes Rav Chaim Pinchas Scheinberg saying that future generations may think that we have had the tradition the entire time. Also, http://www.dailyhalacha.com/displayRead.asp?readID=785&txtSearch=techelet quotes Chacham Ben-tzion Abba Shaul who says that if your father and grandfather didn't wear a string of techelet than you should follow that practice as well. Rav Shlomo Aviner http://www.ravaviner.com/2011/06/techelet.html and in Shu"t She'elat Shlomo 4:12-20 also gives several reasons not to wear techelet.
• Firstly, the discoveries made regarding the Techelet have been inconclusive and the first two claims were later disproved and who’s to say that the new one which is claimed to be authentic will stand the test of time. Additionally, perhaps by the mere fact that for over a thousand years Jews haven’t used such a species for Techelet is a tradition that this species isn’t the correct one. Some sources even point to the fact that the secret of the Techelet was hidden after the destruction of the Bet Hamikdash. Lastly, how are we to determine the correct method in developing the dye if it’s disputed even in the early authorities and the dispute is left unresolved.