How were people saved prior to 33 AD? The exact date isn't important but at some point about 2000 years ago Christ died on a cross. Since that point Christians everywhere have put their faith in Him. He claimed to be the Way, the Truth and the Life and that nobody could get to the Father except through faith in Him (John 14:6).
That's great for everybody since then, but how were people saved before that? There are many more years of history before that date than after. Was there a different savior for them? Did they just believe in God but not in Jesus?
In very broad strokes, what does Christianity say on this matter (general doctrine) and more specifically, are there differing views on this held by major branches of Christianity? If so, what is a summary of the different doctrinal positions?
Before Christ, people were saved by believing in God's promise of the Messiah who was to come, as we are saved by believing in the Messiah who has come.

Hebrews 11:39-40 (ESV)


  And all these [Old Testament saints], though commended through their
  faith, did not receive what was promised, since God had provided
  something better for us, that apart from us they should not be made
  perfect.


There is some speculation that because Jesus is the only way to the Father, OT saints were kept in a comfortable "holding place" (cf. Abraham's bosom in the parable of the rich man), and that when Jesus died he joined them and brought them with him to heaven 

Eph. 4:7-10 (ESV)


  But grace was given to each one of us according to the measure of
  Christ’s gift. Therefore it says, "When he ascended on high he led a host of captives,    and he
  gave gifts to men."
  
  (In saying, "He ascended," what does it mean but that he had also
  descended into the lower regions, the earth? He who descended is the
  one who also ascended far above all the heavens, that he might fill
  all things.)