This paper advocates for a systems theory of algorithms, viewing algorithms as open dynamical systems interacting with other algorithms, physical systems, humans, or databases. Traditional views of algorithms as isolated code are insufficient for modern computational approaches in control, learning, and optimization, where algorithms interact with their environment. The paper argues that systems theory tools are well-suited for addressing algorithmic challenges, and outlines key challenges and opportunities in this domain. The paper presents examples where systems theory has been applied to algorithmic problems, such as the Kalman filter as an online algorithm for least-squares estimation, and discusses the importance of feedback in algorithm design. It also highlights the need for a systems-theoretic approach in analyzing and designing algorithms that operate in real-time, interact with their environment, and handle uncertainty. The paper emphasizes the importance of abstraction, analysis, and design in algorithmic systems theory, and discusses the potential of systems theory in addressing challenges in optimization, machine learning, and control. It also highlights the need for integrating computational, statistical, and complexity theory tools to expand the methodological base of systems theory. The paper concludes with a call for a systems-theoretic perspective on algorithms, emphasizing the importance of feedback, robustness, and the integration of computational and control theory. It also highlights the potential of systems theory in addressing challenges in real-time algorithms, decision-making architectures, and the interaction of algorithms with their environment.This paper advocates for a systems theory of algorithms, viewing algorithms as open dynamical systems interacting with other algorithms, physical systems, humans, or databases. Traditional views of algorithms as isolated code are insufficient for modern computational approaches in control, learning, and optimization, where algorithms interact with their environment. The paper argues that systems theory tools are well-suited for addressing algorithmic challenges, and outlines key challenges and opportunities in this domain. The paper presents examples where systems theory has been applied to algorithmic problems, such as the Kalman filter as an online algorithm for least-squares estimation, and discusses the importance of feedback in algorithm design. It also highlights the need for a systems-theoretic approach in analyzing and designing algorithms that operate in real-time, interact with their environment, and handle uncertainty. The paper emphasizes the importance of abstraction, analysis, and design in algorithmic systems theory, and discusses the potential of systems theory in addressing challenges in optimization, machine learning, and control. It also highlights the need for integrating computational, statistical, and complexity theory tools to expand the methodological base of systems theory. The paper concludes with a call for a systems-theoretic perspective on algorithms, emphasizing the importance of feedback, robustness, and the integration of computational and control theory. It also highlights the potential of systems theory in addressing challenges in real-time algorithms, decision-making architectures, and the interaction of algorithms with their environment.