There many different companies travelling from European cities to Teheran, most of them with stopover somewhere: Turkish, Pegasus, etc.
There are also two almost unknown airlines (not easy to find even on internet) operating direct flights from many cities in Europe:
- Mahan Air: is possible to buy tickets directly on the web site, http://www.mahan.aero/en. Timetable and direct flighs are good points, but prices seem to us a bit expensive
- Iran Air: it is not possible to buy tickets online, you should use contacs on the web site http://www.iranair.co.uk/. We made a request via e-mail, they asked for a document scan. Then we paid via bank transfer and they finally sent us the electronic ticket. It is not a straighforward process, but it was a very good deal as we paid a return direct flight ticket from Italy just 300 euros each .