The topic is much too broad to give a complete treatment in this forum. If you read ‘halachic Hebrew,’ we suggest that you look at the overview found in Techumin.[1] We will give a little background and the bottom line as we see it.
There are two concerns in dealing with sacred texts:
1. There is a Torah prohibition to destroy HaShem’s non-erasable Names.[2] It is a matter of some debate whether destroying other sacred articles, such as a Tanach or even divrei Torah in which HaShem’s Names are not spelled out, is a Torah prohibition or a rabbinic one.[3] Another machloket arises in regard to indirect erasure of a Name. The gemara[4] allows one who had a Name written on his body to enter a bath where the water may dissolve the ink over time, as this is an indirect action (gerama). However, there is reason to believe that this leniency applies only when a variety of mitigating circumstances coincide.[5]
2. One may not disgrace sacred texts and is even required to take steps to save them from disgrace.[6] Similarly, one should avoid writing something sacred that is likely to be disgraced later.[7] The critical need to teach Torah has permitted significant leniency in writing down divrei Torah in a manner that was once forbidden. However, one should take care not to unnecessarily write p’sukim or Names in places where their prospects for proper treatment are poor.[8]
Comparing the two concerns, several important poskim rule that disgrace is a bigger issue than indirect, respectful destruction of the text, at least when HaShem’s Name is not present. Therefore, under certain circumstances, some allowed the burning of divrei Torah in a case where they otherwise could not or would not be buried and would certainly have been desecrated.[9] Much of the discussion dealt with the less severe case of proofs from the printing process, where the texts were never fit for use. The modern alternative to disposal by incineration is putting the texts in recycling bins, which is free of the disrespect of placing the texts in the garbage (even inside a bag). Also, the destruction is indirect, at least from the perspective of the text’s owner. There is room to discuss leniency when Names aren’t involved.[10]
There are discussions regarding material printed by machine with no level or a low level of intention for kedusha and a variety of other questions that raise the possibility that geniza is not always necessary. However, the most accepted halachic approach, to which we subscribe, is that Torah texts of all sorts should normally be put aside for geniza.