The rapid growth of blockchain technologies and decentralized finance has significantly increased the demand for secure interoperability solutions between independent blockchain networks. Cross-chain asset transfer systems, commonly known as blockchain bridges, enable the movement of digital assets and data across multiple blockchain ecosystems, improving scalability, liquidity distribution, and usability of decentralized applications. However, the increasing adoption of cross-chain infrastructures has also introduced substantial security risks. In recent years, bridge-related exploits have resulted in financial losses exceeding billions of US dollars, making interoperability systems one of the most vulnerable components of decentralized ecosystems. This paper analyzes the primary security challenges associated with cross-chain asset transfer systems and examines the architectural characteristics of modern blockchain bridge solutions. The study reviews major bridge architectures, including lock-and-mint bridges, burn-and-release bridges, liquidity pool bridges, validator-based bridges, and light-client bridges. In addition, the paper investigates common attack vectors such as smart contract vulnerabilities, replay attacks, validator compromise, oracle manipulation, multisignature weaknesses, consensus desynchronization, and liquidity draining attacks. The research further evaluates several major bridge exploits, including the Ronin Bridge, Wormhole, and Nomad incidents, in order to identify recurring security weaknesses and operational failures. The paper also discusses mitigation strategies such as decentralized validation mechanisms, threshold signature schemes, formal verification, anomaly detection systems, transaction monitoring, and rate-limiting approaches. Finally, the study explores future research directions related to zero-knowledge interoperability systems, AI-based fraud detection, trust-minimized bridge architectures, and quantum-resistant cryptographic mechanisms. The findings demonstrate that achieving secure and scalable interoperability remains one of the central challenges in modern blockchain infrastructure development.