An increasing number of artificial intelligence (AI) systems are being proposed in ophthalmology, motivated by the variety and amount of clinical and imaging data, as well as their potential benefits at the different stages of patient care. Despite achieving close or even superior performance to that of experts, there is a critical gap between development and integration of AI systems in ophthalmic practice. This work focuses on the importance of trustworthy AI to close that gap. We identify the main aspects or challenges that need to be considered along the AI design pipeline so as to generate systems that meet the requirements to be deemed trustworthy, including those concerning accuracy, resiliency, reliability, safety, and accountability. We elaborate on mechanisms and considerations to address those aspects or challenges, and define the roles and responsibilities of the different stakeholders involved in AI for ophthalmic care, i.e., AI developers, reading centers, healthcare providers, healthcare institutions, ophthalmological societies and working groups or committees, patients, regulatory bodies, and payers. Generating trustworthy AI is not a responsibility of a sole stakeholder. There is an impending necessity for a collaborative approach where the different stakeholders are represented along the AI design pipeline, from the definition of the intended use to post-market surveillance after regulatory approval. This work contributes to establish such multi-stakeholder interaction and the main action points to be taken so that the potential benefits of AI reach real-world ophthalmic settings.