Microarray technology has been widely used in biomedical research to study com plex biological systems and disease processes.Due to its high-dimensionality, new computational and statistical methods and rigorous theoretical development are re quired to draw valid inferences from the data.In this talk, I will present two such problems and the methods and theory that we have developed to address these problems.Both problems can be formulated as variable selection for time-varying coefficient models.The first problem is related to the identification of transcription factors involved in gene regulation during a given biological process based on the time course gene expression data.To capture the dynamic behavior of gene expression, we propose to use a nonparametric varying-coefficient model for such data and present a regularized estimation procedure for variable selection that combines basis function approximations and the smoothly clipped absolute deviation penalty (SCAD).The second problem is related to identify genes with potentially time-varying effects on the risk of cancer recurrence.Our proposed procedures simultaneously select signifi cant variables with time-varying effects and estimate the nonzero smooth coefficient functions.Under suitable conditions, we have established the theoretical properties of our procedure, including consistency in variable selection and the oracle property in estimation.I illustrate these methods with simulations and real data examples.