Randomly-coupled multi-core fiber (MCF) technology has come to attract lots of attention because of its strong applicability to long-haul transmission systems. Compared with weakly-coupled MCFs with independent cores, it can simultaneously realize higher spatial channel density and ultralow transmission loss using existing ultralow-loss single-mode fiber (SMF) core designs. The strong mode coupling characteristics of randomly-coupled MCFs can provide favorable optical properties, such as suppressed accumulation of modal dispersion (MD), mode-dependent loss (MDL), and nonlinear impairments. This article gives an overview of randomly-coupled MCF technology advancements. First, we describe the classification and design of randomly-coupled MCFs and explain what the randomly-coupled MCFs are and how they are designed. State-of-the-art randomly-coupled MCFs can accommodate four, seven, or 12 cores in a standard 125-$\mu \text{m}$cladding while achieving ultralow transmission loss and/or small MD, which are very promising for long-haul transmission media. Next, we present the methods to characterize the optical properties of randomly-coupled MCFs and the difference compared to conventional SMF measurements. We also show the low-loss low-MDL connectivity of this type of MCF and the cabling that can suppress MD. A field-deployed randomly-coupled MCF cable testbed is also presented, which confirmed the favorable optical properties of randomly-coupled MCFs after deployment. Then, multi-core amplifier technologies are briefly summarized, and finally, we discuss the performance improvements in the transmissions over randomly-coupled MCFs and suitable application areas.