Abstract: Recommender system is a type of intelligent platform based on massive dataset mining, which can establish recommendation model, predict users’ preferences on unrated items and achieve individualized information service and strategy support by exploiting the techniques of statistic analyzing, machine learning and artificial intelligence, according to the unique profiles of users and the different characteristics of various items, such as users’ interests, historical consumption behaviors, the quality and the prices of items. Unfortunately, the historical dataset, prediction model and recommendation result are closely related to the users’ privacy. How to provide accurate prediction results under the conditions that the users’ privacy is well protected and the correctness of the recommendation result is efficiently verified becomes a challenging issue. The state-of-the-art mainly focused on solving this problem, by using the techniques of data perturbation and public key fully homomorphic encryption (FHE). However, most of them cannot satisfy all the requirements of accuracy, efficiency and types of privacy preserving required by recommender systems. This article elaborates the existing work from the following four aspects, namely the operation mode, formal security model, the generic constructions of lightweight privacy preserving recommender system and the verification, and the accountability of recommendation results; and identifies the unaddressed challenging problems with convincing solutions. For security models, we focus on formalizing the security models with respect to user data privacy, prediction model privacy and recommendation result privacy, under the standard model or universal composable (UC) model. For efficiency, without exploiting public key FHE, we study the generic constructions of efficient privacy preserving recommender system, respectively in the single user, multiple data setting and the multiple user, multiple data setting, by reducing the usage times of public key encryption and decryption (i.e. only once while it is optimized). Last but not least, we also address the generic theoretical issue of efficient correctness verifiability and auditability for recommendation results, by exploiting the technique of batch verification. All the convincing techniques and solutions discussed above would significantly contribute to both the theoretical breakthrough and the practicability for privacy preserving in recommender systems.