What are the intrinsic connections between economic complexity and sustainability dimensions? To address this question, we have conducted the first Systematic Mapping Study of the literature related to the economic complexity theory, employing databases such as Scopus, Web of Science, and Semantic Scholar following the PRISMA statement complemented with a science mapping technique. Our endeavor has culminated in the compilation of 687 documents published between 2006 and 2022. The findings of this systematic review reveal a thematic and semantic network that interconnects economic complexity with the following dimensions of sustainability: (1) Economic, (2) Social and Human, (3) Environmental, (4) Political, and (5) Cultural. The results offer compelling evidence that research into economic complexity is actively striving to promote studies that are pertinent to the challenges articulated by the 2030 Agenda for Sustainable Development. Furthermore, we propose five avenues for shaping a future research agenda based on the emerging research trends detected through in-depth analysis. In conclusion, we affirm that economic complexity stands as a robust theory that aids in comprehending the multidimensional challenges arising from the pursuit of sustainable development.