Reservoir computing (RC) emerged in the early 2000s, leveraging dynamical systems as reservoirs to adaptively learn spatiotemporal features and hidden patterns in complex time series. Despite its potential for high-precision prediction in chaotic systems, RC faces significant challenges for large-scale industrial adoption. This perspective reviews the progress in mathematical theory, algorithm design, and experimental realizations of RC, identifying emerging opportunities and existing challenges. RC's core idea is to use a dynamical system to generate signal bases from input data and combine them to mimic desired processes. Key aspects include the echo state property, memory capacity, universal approximation theorems, and the design of RC architectures. Physical implementations of RC systems, such as discrete physical nodes, single-node reservoirs, and continuous medium reservoirs, are discussed, highlighting their integration, power consumption, processing speed, and programmability. Applications of RC include signal classification, time series prediction, control of nonlinear dynamical systems, and PDE computations. Despite its strengths, RC faces limitations in tasks like image classification and audio signal processing, where deep learning methods currently outperform RC. Future opportunities for RC include 6G, next-generation optical networks, IoT, green data centers, intelligent robots, and AI for science, with potential to address technical challenges in these domains.Reservoir computing (RC) emerged in the early 2000s, leveraging dynamical systems as reservoirs to adaptively learn spatiotemporal features and hidden patterns in complex time series. Despite its potential for high-precision prediction in chaotic systems, RC faces significant challenges for large-scale industrial adoption. This perspective reviews the progress in mathematical theory, algorithm design, and experimental realizations of RC, identifying emerging opportunities and existing challenges. RC's core idea is to use a dynamical system to generate signal bases from input data and combine them to mimic desired processes. Key aspects include the echo state property, memory capacity, universal approximation theorems, and the design of RC architectures. Physical implementations of RC systems, such as discrete physical nodes, single-node reservoirs, and continuous medium reservoirs, are discussed, highlighting their integration, power consumption, processing speed, and programmability. Applications of RC include signal classification, time series prediction, control of nonlinear dynamical systems, and PDE computations. Despite its strengths, RC faces limitations in tasks like image classification and audio signal processing, where deep learning methods currently outperform RC. Future opportunities for RC include 6G, next-generation optical networks, IoT, green data centers, intelligent robots, and AI for science, with potential to address technical challenges in these domains.