Due to their potential as biomarkers for cancer diagnosis, prognosis, and therapeutics, there is a great demand for accurate quantification and profiling of nucleic acids both for fundamental and clinical research. Multiple cutting-edge technologies (such as real-time reverse transcription PCR, microarray hybridization, and next generation sequencing) have been proposed to carry these tasks; however, all of these techniques face multiple challenges which restrain their use for clinical applications. Among these techniques, nanopore sensors promise the most radical reduction in sequencing time and cost of all current technologies. Counting individual biomolecules through the detection of changes in electrical current produced by charged molecules transiting through them, nanopore devices promise precise, high-throughput sensing with little to no need for pretreatment. However, the involvement of high electric fields and complex ion dynamics presents many drawbacks on both the sensing and profiling fronts.This thesis will focus on the study of several translocation signatures in solid-state nanopores through the use of analytical, continuum, and molecular dynamics modeling. The fundamentals of nucleic acid reactions will be introduced, and new electrokinetic and electrostatic phenomena will be revealed and explored with the over-arching aim of understanding solid-state nanopore translocation dynamics so high-throughput and yet sensitive solid-state nanopore biosensors and sequencing technologies can be realized. A theory for the resistive signal of DNA molecules translocating through a charged nanopore is developed, which is extensively tested against finite element method simulations. This theory allows the prediction of biphasic signals in nanopore devices and provides the needed insight to design nanopores that allow to discriminate between single and double stranded DNA molecules as well as between molecules with different sizes and charge properties. In consistency with molecular dynamics simulations, it also shows that DNA molecules can adsorb into the pore walls, leading to higher current drops (and slower translocation times) than when translocating through the bulk. A theory for the effects of AC and DC electric fields is also proposed, which shows that DNA can undergo significant conformational changes when under the influence of high amplitude – high frequency electric fields. If a double stranded DNA molecule is bound to the pore entrance through the use of field leakage or high surface charges, the applied voltage can denature the DNA molecule (with proper tuning of the pore properties), allowing for different resistive currents depending on the affinity of the DNA to the surface. Molecular tags can be incorporated into this technology, which can lead to precise, easy, low-cost, and high-throughput sensing and profiling of miRNA molecules.