As the Internet of Things (IoT) advances by leaps and bounds, a multitude of devices are becoming interconnected, marking the onset of an era where all things are connected. While this growth opens up opportunities for novel products and applications, it also leads to increased energy demand and battery reliance for IoT devices, creating a significant bottleneck that hinders sustainable progress. At this juncture, backscatter communication (BackCom), as a low-power and passive communication method, emerges as one of the promising solutions to this energy impasse by reducing the manufacturing costs and energy consumption of IoT devices. However, BackCom systems face challenges such as complex interference environments, including direct link interference (DLI) and mutual interference (MI) between tags, which can severely disrupt the efficiency of BackCom networks. Moreover, double-path fading is another major issue that leads to the degraded system performance. To fully unleash the potential of BackComs, the purpose of this paper is to furnish a comprehensive review of existing solutions with a focus on combatting these specific interference challenges and overcoming dual-path fading, offering an insightful analysis and comparison of various strategies for effectively mitigating these issues. Specifically, we begin by introducing the preliminaries for the BackCom, including its history, operating mechanisms, main architectures, etc, providing a foundational understanding of the field. Then, we delve into fundamental issues related to BackCom systems, such as solutions for the DLI, the MI, and the double-path fading. This paper thoroughly provides state-of-the-art advances for each case, particularly highlighting how the latest innovations in theoretical approaches and system design can strategically address these challenges.