From a quick bit of googling there seems to be a divergence between those who believe in a pretribulation rapture (souls being taken up) and more orthodox Christians who simply believe in a single Day of Judgement where everyone will be taken up.
Obviously from an Islamic perspective, we know from the hadith that the last Hour will not arrive until there is no one left in the world praising, glorifying and remembering Allah and that all believers will have passed away beforehand with the 'breeze'.
A curious point is that all the three major religions have the Dajjal [Antichrist] in their traditions and since he has yet to appear, how could the world have ended last Saturday?
Here's the hadith detailing the major signs of the Day of Judgment:The Prophet (saw) said:
"Verily the Hour will never be established until you see ten signs before it."
Then he (saw) mentioned:
the rising of the sun from the west,
the descent of 'Eesaa Ibn Maryam,
Ya'jooj and Ma'jooj,
three tremors (in which the earth will open and swallow those upon it) - one in the east, one in the west and one in the Arabian peninsula.
And the last of them will be a fire that will come out from Yemen, which will drive the people to the (final) place of assembly."