It is difficult to separate this answer from science. Ultimately the discovery, knowledge and theory about dinosaurs is a scientific one; one that is not really discussed in classic Judaic literature due to the discovery of dinosaur fossils begin relatively recent.
Rabbi Slifkin has a chapter devoted to this in 'the Challenge of Creation' (chapter 17 entitled 'Dinosaurs and Sea Monsters').
I will try to summarise some of this chapter:
'And Hashem created the great taninim...' (Bereishit 1:21). Some say that this refers to giant sea monsters, however in Devarim 32:33, where 'tannin' is used in the singular, it refers to snakes. Yechezkel 29:3 they are referred to as crocodiles. Slifkin argues against Schroeder (Science of G-d p.193), who says that taninim refer to the general category of reptiles. Slifkin goes on to argue that the modern term 'reptile' bears no place in classic Judaic thought since the Torah's classification of animals has nothing to do with modern taxonomy that is based on DNA. He argues that claiming that 'taninim' as being dinosaurs is sensationalist, at best. Furthermore, seeing as the majority of dinosaurs were terrestrial, Slifkin questions why the Torah would have made a reference to dinosaurs in general as the sea dwelling 'taninim'.
Slifkin argues that there is 'no reason to expect to find dinosaurs in the Torah any more than we would expect to find ammonites or mammoths'. There are countless species (extinct and present) that bare no necessity that the Torah should find the need to mention them.
He brings another 'contender' for dinosaurs from Iyov (40:15-24):
טו הִנֵּה-נָא בְהֵמוֹת, אֲשֶׁר-עָשִׂיתִי עִמָּךְ; חָצִיר, כַּבָּקָר יֹאכֵל.
טז הִנֵּה-נָא כֹחוֹ בְמָתְנָיו; וְאוֹנוֹ, בִּשְׁרִירֵי בִטְנוֹ.
יז יַחְפֹּץ זְנָבוֹ כְמוֹ-אָרֶז; גִּידֵי פַחֲדָו יְשֹׂרָגוּ.
יח עֲצָמָיו, אֲפִיקֵי נְחֻשָׁה; גְּרָמָיו, כִּמְטִיל בַּרְזֶל.
יט הוּא, רֵאשִׁית דַּרְכֵי-אֵל; הָעֹשׂוֹ, יַגֵּשׁ חַרְבּוֹ.
כ כִּי-בוּל, הָרִים יִשְׂאוּ-לוֹ; וְכָל-חַיַּת הַשָּׂדֶה, יְשַׂחֲקוּ-שָׁם.
כא תַּחַת-צֶאֱלִים יִשְׁכָּב-- בְּסֵתֶר קָנֶה וּבִצָּה.
כב יְסֻכֻּהוּ צֶאֱלִים צִלְלוֹ; יְסֻבּוּהוּ, עַרְבֵי-נָחַל.
כג הֵן יַעֲשֹׁק נָהָר, לֹא יַחְפּוֹז; יִבְטַח, כִּי-יָגִיחַ יַרְדֵּן אֶל-פִּיהוּ.
כד בְּעֵינָיו יִקָּחֶנּוּ; בְּמוֹקְשִׁים, יִנְקָב-אָף.
and in English:
Behold now behemoth, which I made with you; he eats grass like an ox. Behold now, the strength of his loins, and the power in his belly. He thrusts his tail like a cedar, his testicles are bound by twisted cords. His bones are like tubes of bronze; his limbs are like bars of iron. He is the head of the works of G-d; let He who made him bring near His sword to him. The mountains bring him forth food, where all the beasts of the field play. He lies under the shady trees, in the cover of the reeds and swamp. The shady trees cover him with their shadow' the willows of the brook surround him. Behold, he plunders a river without hurry; he trusts that he can draw the Jordan into his mount. He takes in the river with his eyes, his nostrils are as though pierced by hooks.
Slifkin makes reference to a number of creationists that suggest that these verses refer to dinosaurs (saurapods, to be exact), but says that 'no dinosaur lived at the same time as Iyov'. He goes on to suggest that these verses are quite explicitly talking about the hippopotamus.
In summary, he sees no reason for dinosaurs to be mentioned in the Torah.