The task of personalized product search aims at retrieving a ranked list of products given a user's input query and his/her purchase history. To address this task, we propose the PSAM model, a Personalized, Sequential, Attentive and Metric-aware (PSAM) model, that learns the semantic representations of three different categories of entities, i.e., users, queries, and products, based on user sequential purchase historical data and the corresponding sequential queries. Specifically, a query-based attentive LSTM (QA-LSTM) model and an attention mechanism are designed to infer users dynamic embeddings, which is able to capture their short-term and long-term preferences. To obtain more fine-grained embeddings of the three categories of entities, a metric-aware objective is deployed in our model to force the inferred embeddings subject to the triangle inequality, which is a more realistic distance measurement for product search. Experiments conducted on four benchmark datasets show that our PSAM model significantly outperforms the state-of-the-art product search baselines in terms of effectiveness by up to 50.9% improvement under NDCG@20. Our visualization experiments further illustrate that the learned product embeddings are able to distinguish different types of products.