Travelling by train
You can still travel from Europe to Turkey by train, although these days this is more of historical or perhaps even romantic interest than fast or practical. The famed Orient Express from London now travels no further than Vienna, but you can take the daily TransBalkan from Budapest (Hungary) via Bucharest (Romania), a two-night journey with a scheduled 3-hour stop in Bucharest. 1st/2nd class sleepers and couchettes are available, but the train lacks a restaurant car so stock up on supplies. From/to Greek stations there are two daily services, from Istanbul to Pythion every morning and from Istanbul to Thessaloniki every night. There are also daily trains to Istanbul from Sofia (Bulgaria).
There are also once-weekly services from Istanbul to Aleppo and Damascus in Syria, Tabriz and Tehran in Iran.