ABSTRACT Accelerated failure time (AFT) models offer an attractive alternative to Cox proportional hazards models. AFT models are collapsible and, unlike hazard ratios in proportional hazards models, the acceleration factor—a key effect measure in AFT models—is collapsible, meaning its value remains unchanged when adjusting for additional covariates. In addition, AFT models provide an intuitive interpretation directly on the survival time scale. From the recent development of smooth parametric AFT models, we identify potential issues with their applications and note several desired extensions that have not yet been implemented. To enrich this tool and its application in clinical research, we improve the AFT models within a flexible parametric framework in several ways: we adopt monotone natural splines to constrain the log cumulative hazard to be a monotonic function across its support; allow for time‐varying acceleration factors, possibly include cure and accommodating more than one time‐varying effect; and implement both mixture and nonmixture cure models. We implement all of these extensions in the rstpm2 package, which is publicly available on CRAN. Simulations highlight a varying success in estimating cure fractions. However, in terms of covariate‐effect estimation, flexible AFT models appear to be more robust than the Cox model even when there is a high proportion of cured individuals in the data, regardless of whether cure is reached within the observed data. We also apply some of our extensions of AFT models to real‐world survival data.