The molecular characterization of poorly and anaplastic thyroid carcinomas has been greatly improved in the last years following the advent of high throughput technologies. However, with special reference to genomic data, the prevalence of reported alterations is partly affected by classification criteria. The impact of molecular pathology in these tumors is multifaceted and bears diagnostic, prognostic, and predictive implications although its use in the clinical practice is not completely assessed. Genomic profiling data claim that genetic alterations in poorly differentiated and anaplastic thyroid carcinomas include "Early" and "Late" molecular events, which are consistent with a multi-step model of progression. "Early" driver events are mostly RAS and BRAF mutations, whereas "Late" changes include above all TP53 and TERT promoter mutations, as well as dysregulation of gene involved in the cell cycle, chromatin remodeling, histone modifications, and DNA mismatch repair. Gene fusions are rare but represent relevant therapeutic targets. Epigenetic modifications are also playing a relevant role in poorly differentiated and anaplastic thyroid carcinomas, with altered regulation of either genes by methylation/deacetylation or non-coding RNAs. The biological effects of epigenetic modifications are not fully elucidated but interfere with a wide spectrum of cellular functions. From a clinical standpoint, the combination of genomic and epigenetic data shows that several molecular alterations affect druggable cellular pathways in poorly differentiated and anaplastic thyroid carcinomas, although the clinical impact of molecular typing of these tumors in terms of predictive biomarker testing is still under exploration.