Many sectors, like finance, medicine, manufacturing, and education, use blockchain applications to profit from the unique bundle of characteristics of this technology. Blockchain technology (BT) promises benefits in trustability, collaboration, organization, identification, credibility, and transparency. In this paper, we conduct an analysis in which we show how open science can benefit from this technology and its properties. For this, we determined the requirements of an open science ecosystem and compared them with the characteristics of BT to prove that the technology suits as an infrastructure. We also review literature and promising blockchain-based projects for open science to describe the current research situation. To this end, we examine the projects in particular for their relevance and contribution to open science and categorize them afterwards according to their primary purpose. Several of them already provide functionalities that can have a positive impact on current research workflows. So, BT offers promising possibilities for its use in science, but why is it then not used on a large-scale in that area? To answer this question, we point out various shortcomings, challenges, unanswered questions, and research potentials that we found in the literature and identified during our analysis. These topics shall serve as starting points for future research to foster the BT for open science and beyond, especially in the long-term.