Does django with mongodb make migrations a thing of the past?
What does the migration process look like with a non-relational db?

Depends on if you need to update all the existing data or not. 
In many cases, you may not need to touch the old data, such as when adding a new optional field. If that field also has a default value, you may also not need to update the old documents, if your application can handle a missing field correctly. However, if you want to build an index on the new field to be able to search/filter/sort, you need to add the default value back into the old documents.
Something like field renaming (trivial in a relational db, because you only need to update the catalog and not touch any data) is a major undertaking in MongoDB (you need to rewrite all documents).
If you need to update the existing data, you usually have to write a migration function that iterates over all the documents and updates them one by one (although this process can be shared and run in parallel). For large data sets, this can take a lot of time (and space), and you may miss transactions (if you end up with a crashed migration that went half-way through).
Since mongo doesn't have a schema, does that mean that we won't have to do migrations when we change the models?
What does the migration process look like with a non-relational db?