Survival analysis aims to predict the risk of an event, such as death due to cancer, in the presence of censoring. Recent research has shown that existing survival techniques are prone to unintentional biases towards protected attributes such as age, race, and/or gender. For example, censoring assumed to be unrelated to the prognosis and covariates (typically violated in real data) often leads to overestimation and biased survival predictions for different protected groups. In order to attenuate harmful bias and ensure fair survival predictions, we introduce fairness definitions based on survival functions and censoring. We propose novel fair and interpretable survival models which use pseudo valued-based objective functions with fairness definitions as constraints for predicting subject-specific survival probabilities. Experiments on three real-world survival datasets demonstrate that our proposed fair survival models show significant improvement over existing survival techniques in terms of accuracy and fairness measures. We show that our proposed models provide fair predictions for protected attributes under different types and amounts of censoring. Furthermore, we study the interplay between interpretability and fairness; and investigate how fairness and censoring impact survival predictions for different protected attributes.