Motivated by applications of rental services in e-commerce, we consider real-time assortment of reusable products. In our model, arriving consumers with heterogeneous types choose rental products from the offered assortment, pay the rental fees, and return the product to the platform after a rental time. Consumers' types specify their choice models, rental fees and rental time distributions for various products. Our goal is to design competitive online policies against an appropriate benchmark for both the prior-free setting, in which types are arbitrary (or adversarial), and the Bayesian setting, in which types are drawn independently from known distributions.