Abstract:Traditional mathematical models used in designing next-generation communication systems often fall short due to inherent simplifications, narrow scope, and computational limitations. In recent years, the incorporation of deep learning (DL) methodologies into communication systems has made significant progress in system design and performance optimisation. Autoencoders (AEs) have become essential, enabling end-to-end learning that allows for the combined optimisation of transmitters and receivers. Consequently, AEs offer a data-driven methodology capable of bridging the gap between theoretical models and real-world complexities. The paper presents a comprehensive survey of the application of AEs within communication systems, with a particular focus on their architectures, associated challenges, and future directions. We examine 120 recent studies across wireless, optical, semantic, and quantum communication fields, categorising them according to transceiver design, channel modelling, digital signal processing, and computational complexity. This paper further examines the challenges encountered in the implementation of AEs, including the need for extensive training data, the risk of overfitting, and the requirement for differentiable channel models. Through data-driven approaches, AEs provide robust solutions for end-to-end system optimisation, surpassing traditional mathematical models confined by simplifying assumptions. This paper also summarises the computational complexity associated with AE-based systems by conducting an in-depth analysis employing the metric of floating-point operations per second (FLOPS). This analysis encompasses the evaluation of matrix multiplications, bias additions, and activation functions. This survey aims to establish a roadmap for future research, emphasising the transformative potential of AEs in the formulation of next-generation communication systems.