How to glue your LEGO models

Please don't ever use any form of glue on any LEGO pieces, not even glue that claims to dissolve in water.

The whole point of LEGO pieces is to be able to build and rebuild with them producing an infinite number of possible outcomes. If you just want a unchanging built plastic model, there are far better plastic model kits designed for that purpose.

When a LEGO set is glued, nearly all of its value and potential is removed.

There are a couple very specific uses cases for gluing LEGO models. 

Larger sculptures that will be repeatedly shipped to exhibits or be placed where the public can interact with them usually must be glued out of necessity, though we (Music City Bricks) have had sculptures exhibited in reach of visitors for years with no glue required.

Another narrow use case for glue involves severely autistic children that love to play with build LEGO models but have a special one they want to stay together and do not have coping skills to deal with it when it falls apart.

Most LEGO pieces are made with ABS plastic and any solvent, glue, or cement that is designed to work with ABS plastic should work to glue a LEGO model. It is easy to make a real mess of things if you drip any on the model and most solvents and glues require research to see if they are safe around children. It would be good to do a lot of research before gluing your first LEGO model and hopefully your research talks you out of it.