I recently took a round-trip flight using a combination of Virgin Atlantic and Delta airlines. The airlines lost my checked bag on BOTH the departure and return legs of my journey.
I was told by Virgin staff that this has been a persistent problem with their connections with Delta, and one staff member said it happens basically daily at Heathrow (LHR) that Virgin connections with Delta have passengers who's bags do not arrive.
Both airlines have placed blame on one another in their conversations with me.
Let this be a warning: If you are travelling with a combination of Virgin and Delta, they are having problems with the bags not arriving with you! I asked in a written letter to both airlines to tell me how and when they expect the issue to be solved, and I have not received a response to that question.
Also, they will not compensate you for your inconvenience. I will be reimbursed for toiletries and clothes for the few days I was on vacation (a confusing and cumbersome process), but that is not the case upon your return. And you are not compensated for your inconvenience of spending your vacation without your things and the time lost having to replace your clothes and toiletries.
If you are considering taking this flight combination, I would advise you to speak with Delta or Virgin Atlantic directly about this issue first.