Fractional-order systems and controls utilize concepts from fractional calculus for modelling, control designs, and practical applications. However, it can be challenging to transform these memory-dependent systems and controllers into hardware, which is why high-order integer systems are often used instead. Field Programmable Gate Arrays (FPGAs) are ideal for implementing fractional-order systems and controllers. Careful consideration of system quality, hardware cost, and speed is necessary to implement fractional-order systems, such as differentiators, integrators, controllers, and systems. Fortunately, recent technological advancements have made it easier, faster, and less expensive to implement digital hardware for fractional-order systems and controllers. This is mainly because the FPGA platform is a cost-effective and efficient solution for implementing high-quality approximations of fractional order systems with high throughput and short design time. Numerous attempts in the literature have been made to implement fractional-order systems and controllers on FPGAs. This article explores the methods of implementing fractional-order systems and PID controllers via FPGA technology. It briefly explains the definitions, approximations, implementation approaches, software tools, FPGA series, and models used in the literature to implement fractional-order systems and controls using FPGAs. The article also discusses future directions in FPGA implementation of fractional-order systems and controllers, highlights open problems, and offers possible solutions. © 2024 Elsevier GmbH