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Understanding the principles underlying gene expression is crucial for numerous fields, including cancer research, neuroscience, and medicine. Recent advancements in biotechnology, such as single-cell RNA sequencing and spatial transcriptomics, have made it possible to measure gene expression at single-cell resolution and offered new opportunities to quantitatively study gene expression and its relationships to cell phenotypes. The vast amount of transcriptomic data has created a pressing need for novel computational methods to uncover hidden biological insights. While many existing computational approaches focus on distinguishing cell identities based on gene expression profiles, a gap remains in achieving a comprehensive and mechanistic understanding of how and why these differences arise. This dissertation seeks to bridge this gap by addressing three key challenges unique to this domain and summarizing findings from three distinct yet interconnected studies. The first study presents VeloVAE, a variational Bayesian method for recovering temporal information on RNA transcription, splicing, and degradation from single-cell RNA sequencing data. The second study introduces TopoVelo, a graph learning method for uncovering the spatial dynamics of cell migration and differentiation using spatial transcriptomic data. The third study introduces ABCDEFG, a differentiable causal discovery method designed to reveal causal relationships from single-cell perturbation data. These methods integrate deep learning techniques with domain knowledge to extract hidden information from existing biological data. Through a series of studies, we demonstrate that these approaches achieve state-of-the-art performance and effectively capture biological insights related to the temporal, spatial, and causal mechanisms of gene expression.