Open innovation benefits from access to cutting-edge discoveries to increase their transformation into tangible applications for the benefit of society. Improving research quality has been proposed as a primary objective of open science by the United Nations, to increase science reproducibility, impact, and trust, leading to robust decision-making and policies. However, opening access to data and processes is insufficient for researchers to achieve open innovation in the context of globalization, for example, by gathering insights from external and internal sources. Developing the appropriate mindset to manage complexity and generate synergy among researchers in academia, industry, and the government is essential to catalyze knowledge and transform it into relevant innovations for society. To gain insights into the roles and challenges of researchers aiming to bridge the gap between open science and open innovation, a decade-plus Mapping Literature Review was conducted based on the complex thinking paradigm. Complex thinking allows for novel connections of the information collected through open science and open innovation, considering different forms of engaging with alternative means of knowledge creation that may promote innovative and critical thinking. The findings revealed: a) broad positioning of the terms in the European Union; b) open access and open data as current driving themes; c) a constant trade-off between the terms “open data” and “information protection”; d) lack of studies on researchers’ complex thinking to help them manage openness; e) absence of the environmental helix in the initiatives; and (f) challenges in innovative communication and collaborative practices among public and private entities. Overall, we identified an opportunity to develop researchers’ complex thinking such that the openness of information becomes a shared responsibility among partners across multiple helices. This shared responsibility can have methodological implications that permeate how open science and open innovation are theorized and, in practice, facilitate the development of fundamental collaborative research procedures.