Why are the largest animals who ever lived living now?

Some people wonder how we got so lucky as to have the largest animals that ever lived, the blue whales, living now.  After all most of the species that ever existed, existed in the past, why wasn't one of them the largest.  
 
As usual there are probably several factors.  First, it seems likely that there were larger animals in the past.  I know many scientists express great confidence that no animal larger than the blue whales ever existed, but there are reasons to doubt this.  We keep finding larger and larger dinosaurs and some of the largest are getting up into the general size range of the blue whale.