This work focuses on studying properties of DNA molecules and DNA-protein interactions using synthetic nanopores, and it examines the prospects of sequencing DNA using synthetic nanopores. We have developed a method for discriminating between alleles that uses a synthetic nanopore to measure the binding of a restriction enzyme to DNA. There exists a field threshold for rupturing the DNA-protein complex in nanopores, which are larger in diameter than the double helix of a DNA molecule but smaller in diameter than the DNA-protein complex. We relate the binding strength to the field threshold at which the complex dissociates. We also describe a method of measuring the transition from double-stranded (dsDNA) to single-stranded DNA (ssDNA), called the helix-coil transition, which is vital to biology. The force required to dissociate base pairs depends on whether the DNA is unzipped by pulling parallel to the bases or stretched by pulling transverse to the base pairs. We have probed the dichotomy in the force by studying the translocation of hairpin DNA in pores smaller in diameter than dsDNA. Furthermore, we show that it is possible to trap a single dsDNA molecule in a nanopore less than 3 nm in diameter. We use the fact that there is a voltage threshold for dsDNA to permeate a pore with diameter comparable to or smaller than the dsDNA double helix. The molecule is temporarily trapped by first applying a voltage higher than this threshold, and once the molecule is inside the nanopore, the voltage is reduced below the threshold. We have succeeded in trapping a lambda-DNA molecule for seconds in the pore. Moreover, if the duration of the trap is extremely long, we observe what may be signatures of the base pairs translocating through the pore. Finally, we report on our efforts in exploring four strategies for improving the electrical performance by reducing the parasitic membrane capacitances of synthetic nanopores: (1) increasing the thickness of Si[subscript 3] N[subscript 4] membranes; (2) miniaturizing composite membranes consisting of Si[subscript 3] N[subscript 4] and polyimide; (3) miniaturizing membranes formed from metal-oxide-semiconductor (MOS) capacitors; and finally, and (4) compensating for the capacitance through external circuitry. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]