From the Iberian Peninsula alone:

Prehistory - Was it first settled directly from Africa or did humans border the Mediterranean from the east first? - Were neanderthals still around when modern humans moved in (and were therefore the last neanderthals on Earth) or had they already disappeared? - Is the Lagar Velho child a neanderthal-sapiens hybrid? Why is he thousands of years younger than even the latest possible evidence of Iberian neanderthals? - Was the horse domesticated in Iberia independently of Central Asia?

Ancient - Paleohispanic scripts. None deciphered yet. - Were the Tartessian, Iberian and Basque-Aquitanian languages related? How much? Were they related to non-Iberian languages? Which? What languages were spoken in the center and west before the Celts settled there? - Was the Tartessian culture an unified state like the classics say? Where is its capital? Was it swallowed by a tsunami? Did it inspire the Atlantis myth? - Were the Celtiberians a "mixed people" between Celts and Iberians, or were they an earlier wave of Celtic conquerors that were in turn semi-displaced by a second wave (i.e. Celtiberian means "Celt of Iberia", rather than "Celt-Celt")? - Were the Lusitanians Celtic at all? Or descendants of even yet another Indoeuropean invasion predating even the two Celtic ones (assuming there were two)? Were they actually Indoeuropean? - When and how did the Romans conquer the Basque Country? Why did the Basque language survive and not other pre-Roman languages?

Late Roman-Early Medieval - Was the executed Galician heretic Priscilian's body returned to Galicia? Is it actually his body that is in the supposed tomb of St James in Santiago? Did the 'Way of St James' evolve from an earlier Priscilianist pilgrimage? - What happened to the Roman legions in Spain when the first wave of Germanics invaders arrived? - Who and how ruled the Cantabrian coast after the Roman collapse? What exactly is this "Cantabrian senate" that submitted to the Visigoths under King Liuvigild after a campaign in the 6th century? - What are and where were these "Sabaria" and "Orospeda" places that Liuvigild also conquered (and are not mentioned except in texts about his conquests)? - Did the Byzantines really conquer SE Spain or did they just assume control after the Ibero-Roman population rose on their own, successfully, against the Visigoths? Where was the Roman-Visigoth border? Was there a native-ruled independent borderland/buffer state between a Byzantine coast and a Visigothic interior?

Later Medieval - Did Muslim raids happen before 711 or are the mentions of them historiographical errors? - Where was the Battle of Guadalete actually fought at? - What happened to the two Visigothic claimant lines after the Muslim invasion? - Was Pelagius a real person? Did he actually have Visigothic heritage? - Did the "Duero Desert" actually exist? - Who was "Isabel", the third wife of Alfonso VI of Leon? - Who was the shepherd that showed the Christian armies a trail that they could use to ambush the Almohad army at the decisive battle of Las Navas? Where did he come from and where did he go? - Did Ferdinand II of Aragon have Philip the Handsome or the Portuguese heir murdered?