I have two MongoDB collections that share a common _id. Using the mongo shell, I want to find all documents in one collection that do not have a matching _id in the other co
You will have to save the _ids from collection A to not pull them again from collection B, but you can do it using $nin. See Advanced Queries for all of the MongoDB operators.
Your end query, using the example you gave would look something like:
db.Test.find({"_id": {"$nin": [ObjectId("4f08a75f306b428fb9d8bb2e"),
ObjectId("4f08a766306b428fb9d8bb2f")]}})`
Note that this approach won't scale. If you need a solution that scales, you should be setting a flag in collections A and B indicating if the _id is in the other collection and then query off of that instead.
Updated for second part:
The second part is impossible. MongoDB does not support joins or any sort of cross querying between collections in a single query. Querying from one collection, saving the results and then querying from the second is your only choice unless you embed the data in the rows themselves as I mention earlier.