Self-organizing feature maps (SOMs) are commonly used technique for clustering and data dimensionality reduction in many application fields. Indeed, their inherent property of topology preservation and unsupervised learning of processed data without any prior knowledge put them in the front of candidates for data reduction in the Internet of Things (IoT) and big data (BD) technologies. However, the high computational cost of SOMs limits their use to offline approaches and makes the online real-time high-performance SOM processing more challenging and mostly reserved to specific hardware implementations. In this article, we present a survey of hardware (HW) SOM implementations found in the literature so far: the most widely used computing blocks, architectures, design choices, adaptation, and optimization techniques that have been reported in the field of hardware SOMs. Moreover, we give an overview of main challenges and trends for their ubiquitous adoption as hardware accelerators in many application fields. This article is expected to be useful for researchers in the areas of artificial intelligence, hardware architecture, and system design.