Most of the DNA in a prokaryotic cell is accounted for by just one type of circular DNA molecule that is bound by a few proteins to form a nucleoid (sometimes also called a chromosome; a few types of small, extrachromosomal, circular DNA molecule, known as plasmids, may also be found). By comparison, the DNA of eukaryotic cells is much more complex: there are often many different DNA molecules, and they can be immensely long and have diverse functional capabilities. The genome (the collection of different DNA molecules) of a eukaryotic cell is partitioned between at least two types of organelle: a single nucleus and multiple mitochondria. (Plant cells and algae have additional DNA-containing chloroplasts).
Nuclear (chromosomal) DNA
Most of the DNA in a eukaryotic cell is present in the nucleus, distributed between multiple linear chromosomes. The soluble part of the nucleus, the nucleosol, has a nuclear matrix that contains a variety of subnuclear structures lacking membranes (Figure 1A). Pores in the nuclear envelope provide a regulated passageway for molecules to transit between the nucleus and cytoplasm.

Fig1. The structures of the two genome repositories of animal cells. (A) Nuclear structure (left) and details of nuclear lamina and nucleo-cytoplasmic connections (right). Individual chromosomes tend to occupy discrete chromosome territories in interphase nuclei. Readily visible in each nucleus are one or a few nucleoli, regions where chromosomal segments containing rRNA genes are brought together to synthesize and process rRNA. Cajal bodies are sites for assembling small nuclear/nucleolar ribonucleoprotein (snRNP/snoRNP) particles. Fully mature snRNPs assemble at nuclear speckles in readiness for splicing pre-mRNA. PML bodies are composed predominantly of the premyelocytic leukemia protein and are thought to be involved in post-translational control and stress pathways (PMID 2972366). The nuclear lamina, consisting of intermediate filaments (lamins) and lamin-associated membrane proteins, lies on the inner surface of the inner nuclear membrane. It maintains nuclear stability, organizes chromatin, and binds nuclear pore complexes (NPC), nuclear envelope proteins (purple), and transcription factors (pink). Certain chromatin-associated proteins (blue) bind to nuclear envelope proteins. Note that the nuclear envelope is continuous with the endoplasmic reticulum (ER), and that the outer membrane of both of these is studded with ribosomes. (B) Mitochondria have a dynamic structure: they continually fuse and divide, and can develop tubular structures. Their inner membrane forms multiple folds known as cristae (singular crista). (C) Mitochondrial nucleoid organization. Highly schematic representation of a nucleoid (which often contains multiple mtDNA copies rather than the single mtDNA shown here for clarity). Core proteins (shown in orange) are mtDNA-binding proteins that are dominated by the mtDNA packaging protein TFAM. Proteins shown in yellow cannot bind mtDNA directly, but bind to other proteins of the nucleoid. White circles A represent the ATAD3 protein that binds mtDNA directly, and also binds the major core protein to anchor the nucleoid to the inner membrane and to mitochondrial ribosomes. (D) Distribution of nucleoids (green) within tubular mitochondria (red) of a yeast cell (left) and a human fibroblast with its nucleus stained in blue (right). (A [left], reprinted from Lanctô C et al. [2007] Nat Rev Genet 8:104–115; PMID 17230197. With permission from Springer Nature. Copyright © 2007; B and D [left], adapted from Friedman JR & Nunnari J [2014] Nature 505:335–343; PMID 24429632. With permission from Springer Nature. Copyright © 2014; C, adapted from Gilkerson R et al. [2013] Cold Spring Harb Perspect Biol 5:a011080; PMID 23637282. With permission from Cold Spring Harbor Laboratory Press; D [right], from Kukat C et al. [2011] Proc Natl Acad Sci USA 108:13534–13539; PMID 21808029. With permission from the National Academy of Sciences. Copyright 2011, National Academy of Sciences, USA.)
Each chromosome is a single, very long, negatively-charged DNA molecule intricately packaged with positively-charged histone proteins (see below) and various other proteins. The number of different chromosomes (and associated DNA content) varies greatly between species. Because each type of chromosome in a cell contains its own type of DNA molecule there are many different linear DNA molecules in eukaryotic nuclei, each present in a very few copies (most of our cells, for example, have two copies of each chromosome and two copies of the associated DNA molecule).
Mitochondrial DNA The remainder of the DNA is housed in the mitochondria. Mitochondria are often portrayed as static structures, such as in the image in Figure 2, but in reality they seem to be part of a reticular network with long tubules, and there is a continuous process of division and fusion, even in resting cells (Figure 1B).

Fig2. Prokaryotic and eukaryotic cell anatomy. Prokaryotic cells are much smaller than eukaryotic cells and lack the internal organelles found in the latter. The eukaryotic cell shown at the top of this figure is a generic vertebrate cell.
Until quite recently, prokaryotes were simply considered to comprise diverse types of bacteria, but in 1977 phylogenetic studies by Carl Woese indicated that prokaryotes comprise two very different kingdoms or domains of life, as distinct from each other as they are from eukaryotes.
The mitochondrial DNA (mtDNA) differs from nuclear DNA in many respects. Thus, mtDNA molecules are comparatively small, circular DNA molecules and have much less bound protein. Additionally, there is only one type of mtDNA and it is present in many copies per cell (the copy number varies, but many human cells have several thousand copies of a mtDNA molecule).
Whereas chromosomes are units for segregating nuclear DNA, the unit of segregation for mtDNA is the nucleoid, a complex of from one to a few protein-bound mtDNA molecules that binds to the inner face of the inner mitochondrial membrane (Figure 1C). Nucleoids can be seen to be distributed along mitochondrial tubules in suitably stained cells (Figure 1D).