Head and neck squamous cell carcinoma (HNSCC) is one of the most frequent cancers worldwide. The main risk factors are consumption of tobacco products and alcohol, as well as infection with human papilloma virus. Approved therapeutic options comprise surgery, radiation, chemotherapy, targeted therapy through epidermal growth factor receptor inhibition, and immunotherapy, but outcome has remained unsatisfactory due to recurrence rates of ~50% and the frequent occurrence of second primaries. The availability of the human genome sequence at the beginning of the millennium heralded the omics era, in which rapid technological progress has advanced our knowledge of the molecular biology of malignant diseases, including HNSCC, at an unprecedented pace. Initially, microarray-based methods, followed by approaches based on next-generation sequencing, were applied to study the genetics, epigenetics, and gene expression patterns of bulk tumors. More recently, the advent of single-cell RNA sequencing (scRNAseq) and spatial transcriptomics methods has facilitated the investigation of the heterogeneity between and within different cell populations in the tumor microenvironment (e.g., cancer cells, fibroblasts, immune cells, endothelial cells), led to the discovery of novel cell types, and advanced the discovery of cell-cell communication within tumors. This review provides an overview of scRNAseq, spatial transcriptomics, and the associated bioinformatics methods, and summarizes how their application has promoted our understanding of the emergence, composition, progression, and therapy responsiveness of, and intercellular signaling within, HNSCC.