Dinoflagellates are fascinating protists that have attracted researchers from different fields. The free-living species are major primary producers and the cause of harmful algal blooms sometimes associated with red tides. Dinoflagellates lack histones and nucleosomes and present a unique genome and chromosome organization, being considered the only living knockouts of histones. Their plastids contain genes organized in unigenic minicircles. Basic cell structure, biochemistry and molecular phylogeny place the dinoflagellates firmly among the eukaryotes. They have G1-S-G2-M cell cycles, repetitive sequences, ribosomal genes in tandem, nuclear matrix, snRNAs, and eukaryotic cytoplasm, whereas their nuclear DNA is different, from base composition to chromosome organization. They have a high G + C content, highly methylated and rare bases such as 5-hydroxymethyluracil (HOMeU), no TATA boxes, and form distinct interphasic dinochromosomes with a liquid crystalline organization of DNA, stabilized by metal cations and structural RNA. Without histones and with a protein:DNA mass ratio (1:10) lower than prokaryotes, they need a different way of packing their huge amounts of DNA into a functional chromatin. In spite of the high interest in the dinoflagellate system in genetics, molecular and cellular biology, their analysis until now has been very restricted. We review here the main achievements in the characterization of the genome, nucleus and chromosomes in this diversified phylum. The recent discovery of a eukaryotic structural and functional differentiation in the dinochromosomes and of the organization of gene expression in them, demonstrate that in spite of the secondary loss of histones, that produce a lack of nucleosomal and supranucleosomal chromatin organization, they keep a functional nuclear organization closer to eukaryotes than to prokaryotes.