Transformer models have revolutionized AI, enabling applications like content generation and sentiment analysis. However, their use in Machine Learning as a Service (MLaaS) raises significant privacy concerns, as centralized servers process sensitive user data. Private Transformer Inference (PTI) addresses these issues using cryptographic techniques such as Secure Multi-Party Computation (MPC) and Homomorphic Encryption (HE), enabling secure model inference without exposing inputs or models. This paper reviews recent advancements in PTI, analyzing state-of-the-art solutions, their challenges, and potential improvements. We also propose evaluation guidelines to assess resource efficiency and privacy guarantees, aiming to bridge the gap between high-performance inference and data privacy.