Abstract Traditionally, the underlying decision-making algorithms for most real-world systems have been centralized. The term, real-world, refers to systems under computer control that relate to everyday life, are beneficial to the society in the large, and are generally large-scale in scope. Examples include AT&T's dynamic non-hierarchical routing (DNHR) for routing telephone calls, the North American advanced train control system (ATCS) for routing railways, the Swiss banking system (SIC), and inventory management algorithms. While centralized algorithms are simple, easy to conceive and implement, they execute sequentially on uniprocessors and are slow. In addition, by their very nature, centralized algorithms are highly susceptible to natural and artificial disasters. Synchronous distributed algorithms constitute a performance improvement over centralized algorithms, and have been used in fault simulation within the discipline of computer-aided design of digital systems and in matrix manipulations. However, their performance is limited due to frequent inherent synchronizations. This paper critically examines the nature of large-scale, real-world systems and observes that, fundamentally, most complex systems are composed of entities – concurrent, independent, and self-contained units of decision-making, that interact with each other, asynchronously. This paper presents a new class of algorithms – asynchronous, distributed, decision-making (ADDM) algorithms, to constitute the underlying control of such systems. While ADDM algorithms are closely related to autonomous decentralized systems (ADS) in the principal elements, their characteristics and boundaries are defined rigorously. While ADDM algorithms are difficult to conceive, design, and implement, they constitute the natural and logical choice for systems control, and hold the promise of extracting the maximal parallelism inherent in these systems. In addition, in principle, true asynchronous systems can be described accurately only by asynchronous, distributed algorithms, never by synchronous distributed algorithms. This paper reasons the nature of most complex real-world systems from first principles and reasons for its increasing importance in the design of future, large-scale, systems. It then presents the underlying principle of ADDM algorithms, details their fundamental characteristics, enumerates a number of successful ADDM algorithms for problems from different disciplines, and briefly reviews the nature of three of them – (1) real-time, domestic payments processing system, (2) distributed scheduling in railway networks, and (3) distributed routing in ATM networks.