Have some countries or geographical locations that are currently widely considered as "European" been left out in some definitions of Europe?
This question isn't so cut and dry mostly because distinction of is/is not Europe didn't matter to some people/civilizations or the words didn't hold the same kind of value as today. On top of this knowledge of large portions of Europe and Asia were barely known if at all for Early Romans and the Ancient Greeks.
For example it's very likely Early Romans and Greeks had no or very little knowledge of the British Isles, Scandinavia and Iceland. Map recreation based on descriptions from Herodotus in the 5th Century BCE. Herodotus in Histories (~440 BCE) claimed Asia was Anatolia and all holdings of the Persian empire Source Book IV Artlicles 37-40 if you search Asia on that page you will find Book IV article 37 with the 63rd occurrence. As well as defined Europe as such.
- As to Europe, however, it is clearly not known by any, either as regards the parts which are towards the rising sun or those towards the North, whether it be surrounded by sea: but in length it is known to stretch along by both the other divisions. And I am not able to understand for what reason it is that to the Earth, which is one, three different names are given derived from women, and why there were set as boundaries to divide it the river Nile of Egypt and the Phasis in Colchis (or as some say the Maiotian river Tanaïs and the Kimmerian ferry); nor can I learn who those persons were who made the boundaries, or for what reason they gave the names. Libya indeed is said by most of the Hellenes to have its name from Libya a woman of that country, and Asia from the wife of Prometheus: but this last name is claimed by the Lydians, who say that Asia has been called after Asias the son of Cotys the son of Manes, and not from Asia the wife of Prometheus; and from him too they say the Asian tribe in Sardis has its name. As to Europe however, it is neither known by any man whether it is surrounded by sea, nor does it appear whence it got this name or who he was who gave it, unless we shall say that the land received its name from Europa the Tyrian; and if so, it would appear that before this it was nameless like the rest. She however evidently belongs to Asia and did not come to this land which is now called by the Hellenes Europe, but only from Phenicia to Crete, and from Crete to Lykia. Let this suffice now which has been said about these matters; for we will adopt those which are commonly accepted of the accounts.
As can be seen in that text the exact borders of Europe at that time was either unknown or debated with a few possible cutoff points such as the Tanaïs River (Don River) or the Phasis River (Rioni River). Also given Herodotus's wording it's not entirely clear if islands such as Crete, Rhodes and Cyprus would be considered Asia, Europe or something else entirely.
This gets even more muddied when we consider Civilizations who's basis was outside of Europe especially civilizations that pre-date the Greek terms for the continents. Ancient Egyptian (think 3,000 to 5,000 years ago), Assyrian and Babylonian knowledge of Europe would likely have been extremely poor and more or less limited to Greece and the edges of the Black sea so definitions of Continents probably didn't exist let alone mattered to them anymore than saying I'm from X region or going to X region.
Strabo in 7 BCE defined the Edges of Europe and Asia north of the Black Sea at the Don River. Book 11 Chapter 1 Article 1
Going forward into the 9th century the term Europe began to mean Europe but under the influence of the Western Catholic church and became more prominent around the time of the Schism. It's not entirely clear exactly when this fell out of favor and how wide spread this definition really was, so take this one with a grain of salt.
From this point on the definition of what is Europe was largely the same as today with minor variations such as the inclusion of Iceland and the moving of the border to the Volga River + Ural mountains rather than the Don River. Also not entirely clear if Greenland ever was considered part of Europe or not or if anyone cared about the distinction of Greenland as North American or European until the last couple hundred years.
*edit made for a couple spelling mistakes
