Are you looking for promotions that has been applied to the cart with 

promotionEngine.Run(cart)

?

In that case, the promotions that yielded rewards will be stored in the orderform as IOrderForm.PromotionInformation and there you can find an Entries field which has information about which entries and how much was saved per discount.

Correction: it's IOrderForm.Promotions, which is a collection of PromotionInformation. 

I am looking for a way of iterating over the items in the cart and read out their respective promotion. An example look for the site would be:

• Door 1     Price : 10$
  • 50% off
• Door 3     Price : 50$
  • 50% off
• Mailbox    Price : 10$
  • 90% off

• Total saved 39$
• Total 31$

I have managed to get the promotions in a single, encapsulated variable, separated from all the items.

I want to see what promotions are added for each of the items, instead of a collection of promotions added to the cart.

Haven't run this code, but something like this?

var form = cart.GetFirstForm();
var lineItems = cart.GetFirstForm().GetAllLineItems();
foreach (var lineItem in lineItems)
{
    var promotions = form.Promotions.Where(promotionInformation => promotionInformation.Entries.Select(promotionEntry => promotionEntry.EntryCode).Contains(lineItem.Code));
    // This lineitem has been rewarded the above list of promotions
}

Great, that seemed to do the trick Joel!