Archaic admixture is increasingly recognized as an important source of diversity in modern humans, and Neanderthal haplotypes cover 1%-3% of the genome of present-day Eurasians. Recent work has shown that archaic introgression has contributed to human phenotypic diversity, mostly through the regulation of gene expression. Yet the mechanisms through which archaic variants alter gene expression and the forces driving the introgression landscape at regulatory regions remain elusive. Here, we explored the impact of archaic introgression on transcriptional and post-transcriptional regulation. We focused on promoters and enhancers across 127 different tissues as well as on microRNA (miRNA)-mediated regulation. Although miRNAs themselves harbor few archaic variants, we found that some of these variants may have a strong impact on miRNA-mediated gene regulation. Enhancers were by far the regulatory elements most affected by archaic introgression: up to one-third of the tissues we tested presented significant enrichments. Specifically, we found strong enrichments of archaic variants in adipose-related tissues and primary T cells, even after accounting for various genomic and evolutionary confounders such as recombination rate and background selection. Interestingly, we identified signatures of adaptive introgression at enhancers of some key regulators of adipogenesis, raising the interesting hypothesis of a possible adaptation of early Eurasians to colder climates. Collectively, this study sheds new light on the mechanisms through which archaic admixture has impacted gene regulation in Eurasians and, more generally, increases our understanding of the contribution of Neanderthals to the regulation of acquired immunity and adipose homeostasis in modern humans.