Taḥrīf (Arabic: تحريف, "distortion, alteration") is an Arabic term used by Muslims for the alterations which Islamic tradition claims Jews and Christians have made to the revealed books, specifically those that make up the Tawrat (or Torah), Zabur (possibly Psalms) and Injil (or Gospel).
The theme of tahrif was first characterised in the writings of Ibn Hazm (10th century), who rejected claims of Mosaic authorship and posited that Ezra was the author of the Torah. He also systematically organised the arguments against the authenticity of the Biblical text in the first (Tanakh) and second part (New Testament) of his book: chronological and geographical inaccuracies and contradictions; theological impossibilities (anthropomorphic expressions, stories of fornication and whoredom, and the attributing of sins to prophets), as well as lack of reliable transmission (tawatur) of the text. He explains how the falsification of the Torah could have taken place while there existed only one copy of the Torah kept by the Aaronic priesthood of the Temple in Jerusalem. Ibn Hazm's arguments had a major impact upon Muslim literature and scholars, and the themes which he raised with regard to tahrif and other polemical ideas were modified only slightly by some later authors.
Here are some of the relevant verses from Quran itself. They fall in different categories as mentioned by Islahi above.
1. So woe to their learned people, who write the law with their own hands and then say to the people, "This is from Allah," so that they might gain some paltry worldly end. (They do not see that) this writing of their hands will bring woe to them and what they gain thereby will lead to their ruin. Baqra:79
2. O Muslims, do you then expect that these people will accept your invitation and become believers? whereas there have always been among them some who have been hearing the Word of God, understanding it well and then perverting and tampering with it knowingly. Baqra:75
3. Then, for their breach of the covenant We cast them away from Our mercy and caused their hearts to harden. (And now they are in such a state that) they pervert the words from their context and thus distort their meaning, and have forgotten a good portion of the teaching they were imparted, and regarding all except a few of them you continue to learn that they committed acts of treachery. Pardon them, then, and overlook their deeds. Surely Allah loves those who do good deeds. Al Maeda:13
4. And they do not assign to Allah the attributes due to Him when they say: Allah has not revealed anything to a mortal. Say: Who revealed the Book which Musa brought, a light and a guidance to men, which you make into scattered writings which you show while you conceal much? And you were taught what you did not know, (neither) you nor your fathers. Say: Allah then leave them sporting in their vain discourses. Al Inaam:91
5. And there is a party among them who twist their tongues while reciting the Book to make you think that it is part of the Book when in fact it is not. They say: 'It is from Allah', when in fact it is not from Allah. They falsely fix a lie upon Allah, and do so wittingly. Aale Imraan:78