We are commanded to eradicate the nation of Amalek, wiping any vestige of them from the face of the Earth. The reason, as discussed in the previous mitzvah, is because of the cowardly attack that the Amalekites made against God when He took the Jews out of Egypt. Apparently, God knows that certain traits are ingrained within the descendants of Amalek. Nevertheless, many people find this to be a very troubling mitzvah. As historic victims of inquisitions and pogroms, they ask, don't we find it inconsistent to justify genocide?
We can understand this mitzvah better if we realize that the Amalekites had the opportunity to turn their backs on the ways of their nation and be spared their fate. (This is very different from the way in which Jews were treated in, say, the Holocaust.) As with other nations, Amalek had the opportunity to accept the seven univeral (Noachide) laws and submit to Israel's rule. Not only that, they could convert. The Talmud in Gittin (57b) famously tells us that Haman had descendants who taught Torah in B'nei Brak. (Many authorities believe this to include the renowned sage Rabbi Akiva, who was known to be from B'nei Brak and who was descended from converts.)
This mitzvah applies in all times and places. It is discussed in the Talmud in tractate Sanhedrin (20b) and is codified in the Mishneh Torah in the fifth chapter of Hilchos Melachim. This mitzvah is #188 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos and #77 of the 77 positive mitzvos that can be observed today as listed in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.