Eukaryotic chromatin is a hierarchical collection of nucleoprotein structures that package DNA to form chromosomes. The initial levels of packaging include folding of long strings of nucleosomes into secondary structures and array-array association into higher-order tertiary chromatin structures. The core histone tail domains are required for the assembly of higher-order structures and mediate short- and long-range intra- and inter-nucleosome interactions with both DNA and protein targets to direct their assembly. However, important details of these interactions remain unclear and are a subject of much interest and recent investigations. Here, we review work defining the interactions of the histone N-terminal tails with DNA and protein targets relevant to chromatin higher-order structures, with a specific emphasis on the contributions of H3 and H4 tails to oligonucleosome folding and stabilization. We evaluate both classic and recent experiments determining tail structures, effect of tail cleavage/loss, and posttranslational modifications of the tails on nucleosomes and nucleosome arrays, as well as inter-nucleosomal and inter-array interactions of the H3 and H4 N-terminal tails.