In an era where misinformation spreads freely, fact-checking (FC) plays a crucial role in verifying claims and promoting reliable information. While automated fact-checking (AFC) has advanced significantly, existing systems remain vulnerable to adversarial attacks that manipulate or generate claims, evidence, or claim-evidence pairs. These attacks can distort the truth, mislead decision-makers, and ultimately undermine the reliability of FC models. Despite growing research interest in adversarial attacks against AFC systems, a comprehensive, holistic overview of key challenges remains lacking. These challenges include understanding attack strategies, assessing the resilience of current models, and identifying ways to enhance robustness. This survey provides the first in-depth review of adversarial attacks targeting FC, categorizing existing attack methodologies and evaluating their impact on AFC systems. Additionally, we examine recent advancements in adversary-aware defenses and highlight open research questions that require further exploration. Our findings underscore the urgent need for resilient FC frameworks capable of withstanding adversarial manipulations in pursuit of preserving high verification accuracy.