Student opinions for a course are important to educators and administrators, regardless of the type of the course or the institution. Reading and manually analyzing open-ended feedback becomes infeasible for massive volumes of comments at institution level or online forums. In this paper, we collected and pre-processed a large number of course reviews publicly available online. We applied machine learning techniques with the goal to gain insight into student sentiments and topics. Specifically, we utilized current Natural Language Processing (NLP) techniques, such as word embeddings and deep neural networks, and state-of-the-art BERT (Bidirectional Encoder Representations from Transformers), RoBERTa (Robustly optimized BERT approach) and XLNet (Generalized Auto-regression Pre-training). We performed extensive experimentation to compare these techniques versus traditional approaches. This comparative study demonstrates how to apply modern machine learning approaches for sentiment polarity extraction and topic-based classification utilizing course feedback. For sentiment polarity, the top model was RoBERTa with 95.5% accuracy and 84.7% F1-macro, while for topic classification, an SVM (Support Vector Machine) was the top classifier with 79.8% accuracy and 80.6% F1-macro. We also provided an in-depth exploration of the effect of certain hyperparameters on the model performance and discussed our observations. These findings can be used by institutions and course providers as a guide for analyzing their own course feedback using NLP models towards self-evaluation and improvement.