Recurrent events are commonly encountered in medical and epidemiological studies. It is often of interest what and how risk factors influence the occurrence of events. While most existing work on recurrent events address both time-independent and time-dependent effects, our challenges in analyzing a real-world vaccine trial data emphasize the importance of considering scenarios where these effects vary with specific covariates. In this dissertation, we develop novel estimation and inference procedures of two intensity models for recurrent event data. Both models allow for the simultaneous measurement of time-varying and covariate-varying effects, with covariates potentially depend on event history.In the first project, we consider a generalized class of semiparametric intensity models. The models feature unspecific time-varying effects, while covariate-varying and event history effects are modeled parametrically. The models offer much flexibility through the choice of different link functions and parametric functions. Estimation procedures are investigated through local linear approximation and profile log-likelihood method. A cross-validation bandwidth selection method is discussed. Asymptotic properties of estimators are explored using martingale theory and empirical processes. Two hypothesis tests based on the martingale residual have been developed to assess the parametric functions of the covariate-varying effects. A Gaussian multiplier method has been derived to approximate the underlying distribution of test statistics.In the second project, we propose a nonparametric intensity model with frailty that captures unspecified time-varying and covariate-varying effects. Each individual is associated with a frailty term following a Gamma distribution, which acts multiplicatively on the intensity function. We develop maximum likelihood estimation procedure using local linear approximation method with double kernels. The maximization is achieved through an EM algorithm. Variance estimators are obtained using a weighted bootstrap procedure. The simulation studies reveal the satisfactory performance of both models, which have subsequently been employed to analyze the MAL-094 malaria vaccine efficacy trial data. Our data applications demonstrate that these proposed models successfully address the questions raised by the MAL-094 malaria vaccine efficacy trial data.