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This thesis investigates the relatively understudied task of translating Greek(medium-resource language) slang and idiomatic expressions. While MachineTranslation (MT) has made significant advancements over the past decade —firstthrough Neural Machine Translation (NMT) and later with Large Language Mod-els (LLMs)—, its effectiveness remains underexplored for informal and culturallyspecific linguistic constructions, especially in under-resourced settings. Thiswork addresses these challenges by creating two novel parallel Greek-Englishdatasets: one for slang and one for idioms, and testing three LLMs (Gemma, Llama, Mistral) and one NMT model (Helsinki). To probe the models’ knowledge,both datasets are also manually annotated with \"informativeness\" scores with theassistance of human participants, with them indicating how easily the meaningof a target expression can be inferred in a given context. An error analysis is alsoconducted to identify specific model weaknesses. Results show consistently poortranslation performance across all models, for both datasets, with no statisticallysignificant differences among them. However, localized differences in handlinginformativeness and substantial variation in error types are observed. Thesefindings align with existing research highlighting the challenges of translatingunder-resourced languages and culturally embedded expressions.