Fully Homomorphic Encryption (FHE) enables secure computation on encrypted data, preserving confidentiality without requiring decryption. However, FHE alone cannot guarantee the integrity of results computed by potentially untrusted servers, necessitating mechanisms to verify correctness. Succinct Non-Interactive Arguments of Knowledge (SNARKs) have emerged as a powerful tool to address this challenge, enabling efficient verification of computations while maintaining data privacy. This paper provides a systematization of knowledge (SoK) of SNARK-based approaches for verifiable FHE, focusing on recent advancements in designing SNARK-friendly homomorphic schemes and the integration of homomorphic signatures and Message Authentication Codes (MACs), many of which leverage SNARKs for enhanced security. We analyze the trade-offs between privacy, efficiency, and compatibility with modern FHE schemes, offering insights into their practical deployment. Our SoK highlights the transformative potential of these techniques for privacy-preserving applications, including secure cloud computing, machine learning, and distributed data processing.