Data-driven machine learning is the method of choice for predicting molecular phenotypes from nucleotide sequence, modeling gene expression events including protein-DNA binding, chromatin states as well as mRNA and protein levels. Deep neural networks automatically learn informative sequence representations and interpreting them enables us to improve our understanding of the regulatory code governing gene expression. Here, we review the latest developments that apply shallow or deep learning to quantify molecular phenotypes and decode the cis-regulatory grammar from prokaryotic and eukaryotic sequencing data. Our approach is to build from the ground up, first focusing on the initiating protein-DNA interactions, then specific coding and non-coding regions, and finally on advances that combine multiple parts of the gene and mRNA regulatory structures, achieving unprecedented performance. We thus provide a quantitative view of gene expression regulation from nucleotide sequence, concluding with an information-centric overview of the central dogma of molecular biology.