Dan,
Models are sort of backwardly compatible, but only if you save the toolbox to an older format.
If you right click ON THE TOOLBOX in Catalog (your reply to Dan above suggests you were looking within modelbuilder itself) you can SAVE AS. So if you had been creating a model in ArcGIS 10.3 but a client is using 10.1 then if you save the toolbox as 10.1 they will at least be able to see the model.
Now...
This does not necessarily mean the model will work:
- You may have used a tool that they have no license for
- You may have used a tool that does not exist in earlier versions of ArcGIS
- You may have used a script tool that uses python modules that do not exist on their system
I have found that sometime they may need to go into model builder and validate the model, this often clears the red cross which sometimes appears.