What is the Torah view on the dinosaurs? There's no mention of them in the Torah, only that the world was created in 6 days. If they existed, Adam and his descendants should have seen them. Yet there's no mention. Yet we know they lived since we find their bones. One cannot say they lived before Adam since the world existed only 5 days before him.
In the sefer "Q&A Thursday Nights With Rabbi Avigdor Miller" Volume 2, pg 284, he was asked why were the dinosaurs and the mastodon not saved from the mabul? He answered simply because there was no room for them on the teivah (ark) .He said that all species fit but the extra big ones simply didn't fit.
Taninim Hagedolim can possibly mean dinosaurs. The word Tanin means a reptile or serpent (like when Aharon's stick become a sepent - Vayehi l'tanin. The dinosaurs were reptiles. See Dr. Schroeder's "The Science of G-d" which discusses this.
Prof. Nathan Aviezer wrote a book "בראשית ברא" answering questions about the creation in torah view.
There he claims the 6 days of creation to be 6 periods of time that didn't necessarily last 24 hours. Moreover - maybe it was one cycle of dark&light, but thing happened at a quicker pace.
Take, for example, a person's growth. If you were to calculate the rate of growth during his first two years, you would conclude that at the age of 20 he'd be as tall as a skyscraper. Similarly, scientists calculate age of things according to he worlds' pace today, but things may have worked differently in the past.
Hence, dinosaurs might have lived and died prior to Adam Harishon. Maybe created on "day" 5 and extinct before 6.
(Somewhat related: What is the meaning of יוֹם (yowm) in Bereshit?)
The Malbim (on Noach 7:23) addresses "large animals" that couldn't be "wiped out" by the flood, but were buried in depths of the earth following quakes the Mabul created. He is clearly addressing dinosaurs since he's talking about (my free translation): "... geologists who dig and find large animals who have become extinct, they use this to show earth existed long before Bereshis creation..."
Some attribute "התנינים הגדולים" (Bereshis 1:21) to the dinosaurs as a reference of their existing (not mentioned in Malbim).
Another opinion I've heard from reliable people (suggested by the Lubavitcher Rebbe in this letter) is that the world was created "old", such as Adam Harishon was created as a man of 20 and not a newborn baby. Hence, dinosaurs could have either existed - or their remains and footprints were melded into the creation.