X.509 certificates are used to confirm the identity of the parties involved in the communication and to validate the information being transferred. Currently, more and more people and organizations are using X.509 certificates to prove their identities in online transactions, so the reliability and trust level of these certificates come into question. To solve this question in X.509 Certificates trust model many authors proposed their ideas in their research. In this paper we did survey of different research papers which help in giving answer to the question of X.509 certificates trust model and describe these papers in briefly with their advantages and disadvantages. We also describe the terms and concepts comes in understanding of x.509 certificates.