Recent regulations on the Right to be Forgotten have greatly influenced the way of running a recommender system, because users now have the right to withdraw their private data. Besides simply deleting the target data in the database, unlearning the associated data lineage e.g., the learned personal features and preferences in the model, is also necessary for data withdrawal. Existing unlearning methods are mainly devised for generalized machine learning models in classification tasks. In this paper, we first identify two main disadvantages of directly applying existing unlearning methods in the context of recommendation, i.e., (i) unsatisfactory efficiency for large-scale recommendation models and (ii) destruction of collaboration across users and items. To tackle the above issues, we propose an extra-efficient recommendation unlearning method based on Selective and Collaborative Influence Function (SCIF). Our proposed method can (i) avoid any kind of retraining which is computationally prohibitive for large-scale systems, (ii) further enhance efficiency by selectively updating user embedding and (iii) preserve the collaboration across the remaining users and items. Furthermore, in order to evaluate the unlearning completeness, we define a Membership Inference Oracle (MIO), which can justify whether the unlearned data points were in the training set of the model, i.e., whether a data point was completely unlearned. Extensive experiments on two benchmark datasets demonstrate that our proposed method can not only greatly enhance unlearning efficiency, but also achieve adequate unlearning completeness. More importantly, our proposed method outperforms the state-of-the-art unlearning method regarding comprehensive recommendation metrics.