Recurrent events arise in many follow-up and surveillance studies where the observation of recurrent events is terminated by a failure event or censoring. We consider modeling and estimation of recurrent events, possibly together with markers, by forward, backward and failure-time-adjusted process models: (1) Forward recurrent event process starts at a time origin, 0, and moves forward along time t. (2) Backward recurrent event process considers the failure event as the time origin and counts time backward. (3) Failure-time-adjusted process model uses failure-time to adjust recurrent event frequency in modeling. In this talk we will characterize and interpret the three different types of models, discuss statistical challenges for each model, and present some methods and data applications.