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Established guidelines describe minimum requirements for reporting algorithms in healthcare; it is equally important to objectify the characteristics of ideal algorithms that confer maximum potential benefits to patients, clinicians, and investigators. We propose a framework for ideal algorithms, including 6 desiderata: explainable (convey the relative importance of features in determining outputs), dynamic (capture temporal changes in physiologic signals and clinical events), precise (use high-resolution, multimodal data and aptly complex architecture), autonomous (learn with minimal supervision and execute without human input), fair (evaluate and mitigate implicit bias and social inequity), and reproducible (validated externally and prospectively and shared with academic communities). We present an ideal algorithms checklist and apply it to highly cited algorithms. Strategies and tools such as the predictive, descriptive, relevant (PDR) framework, the Standard Protocol Items: Recommendations for Interventional Trials-Artificial Intelligence (SPIRIT-AI) extension, sparse regression methods, and minimizing concept drift can help healthcare algorithms achieve these objectives, toward ideal algorithms in healthcare.