After an introduction to the structure of nucleic acids DNA and RNA, we will focus on periodic and aperiodic (quasi periodic, fractal and random) nucleotide sequences. We will give some attention to genetically determined sequences. We discern charge transfer from charge transport. We give prominence to the role of trimers or codons. We discern coherent processes (quantum transmission) from incoherent or thermal processes (hopping). We will describe our methods, i.e., tight binding (TB) variants (coarse grained or at the atomic level) and based on density functional theory (DFT). Next, we will present results [1, 2, 3, 4] concerning charge transfer and transport in periodic and aperiodic nucleotide sequences. Finally, we will give an overview.