Quantile regression provides a more comprehensive relationship between a response and covariates of interest compared to mean regression and is especially advantageous for censored data as it substantially generalizes classical survival models such as the AFT model. In this talk, I will first discuss a new Bayesian approach for censored quantile regression that can handle high dimensional covariates. Our approach uses continuous spike and slab priors with sample size dependent parameters to induce adaptive shrinkage and sparsity. A scalable Gibbs sampling algorithm for posterior computation will be presented, which has desired theoretical properties. I will also briefly describe a new data augmentation method for estimation in censored quantile regression that can handle arbitrary types of censoring.