Striving towards globally-inclusive models, much effort has been spent on increasing the multilingual capabilities of language technology. However, even large language models still cover major languages only, and knowledge on the effects of their language capabilities in integrated scenarios (e.g., in vision-language models) is rather rare. Additionally, research on multilingual natural language processing has for long ignored other aspects relevant to global inclusion that transcend the surface level-form of languages (e.g., cultural values). In this talk, I will present some of our works showcasing these issues — towards a joint discussion on globally-inclusive language technologies.