One of the places the Phoenicians colonized was the Mediterranean side of Spain, and their writing system spread around that peninsula. Like in Italy, there were quite a few different, mostly related scripts. Unlike in Italy, there wasn’t a hugely successful culture in the vicinity which talked about its neighbours and whose manuscripts got copied and recopied by monks in later years; their own writers also didn’t leave as much behind. Less is known about the tribes on the Iberian peninsula than the Italian one.
The scripts that are best understood are the Levantine scripts, which descended from Phoenician. There is a northern set and a southern set, but their differences are — scholars believe — mostly just in glyph shape, not in the fundamental structure. (The Celtiberian branch in the northeast dropped two characters.)
While these scripts are clearly the children of Phoenician, Phoenician might not be all that eager to claim them. Indeed, they might look like Phoenician, but they act very differently. Instead of being an abjad like their parent, instead of being a forward-looking syllabary or even one o’ them avant-guard alphabets, these scripts are a bastard love-child combination of syllabary and alphabet. They have vowels! They have consonants! They have syllables!
All the vowels have their own glyphs. All of the consonants that you can say continuously (the continuants, like “m”, “l”, and “r”) are individual letters. All the ones that you can’t (the occlusives, like “b”, “k”, and “t”) only get a glyph if they are paired with a vowel. For example, you have glyphs for “a”, “m”, and “ba”, but not for “b” or “ma”.
Greek script was also used on the Iberian peninsula, with almost no change. They left some letters out and included a short vertical mark to the “r” symbol to make it “trilled r”. It’s most striking feature is how few letters it has: sixteen, fifteen if you consider the trill mark as a modifier and count the trilled “r” glyph as the same as the untrilled “r” glyph.