Solid-state nanopores are a versatile class single-molecule sensors to electrically characterize a range of biological molecules. Nanopores operate on the simple premise that when a voltage is applied across a pore immersed in a salt solution, the passage of a biomolecule results in a transient blockage in the ionic current that provide information about the translocating molecule. This thesis presents studies employing various DNA nanostructures with solid-state nanopore electrical readout for the development of high sensitivity digital single-molecule assays to detect low-abundance biomarkers. Toward this ultimate goal, work presented in this thesis use nanopores to probe DNA nanostructures, their assembly, mechanical properties, and monitor their dynamics with time and temperature. DNA nanostructures are self-assembled via specific base pairing of DNA, their programmability make them particularly useful for applications including drug delivery, molecular computation and biosensing. Here, I first show results of translocation profiles and discuss folding characteristics, mobility, and molecular configuration during passage for different DNA nanostructures such as the short star-shaped DNA nanostructures and large helix-bundle DNA origami structures under various experimental conditions in an effort to understand the passage characteristics through nanopores of these structures before using them in biological assays. I conclude by presenting a magnetic bead-based immunoassay scheme using a digital solid-state nanopore readout. Nanopore has the ability to count molecules one at a time, this allows accurate and precise determination of the concentration of a biomarker in solution. Coupled with the use of specific choice of DNA nanostructures, as proxy labels for proteins of interest, I establish that nanopores sensors can reliably quantify the concentration of a protein biomarker from complex biofluids and overcome the traditional challenges associated with nanopore-based protein sensing, such as specificity, sensitivity, and consistency. I demonstrate the quantification of thyroid stimulating hormone (TSH) with a high degree of precision down to the femtomolar range by using a nanoparticle-based signal amplification strategy. The proposed assay scheme is generalizable to a framework for the detection and quantification of a wide range of target proteins, and given that its performance can further be improved with the use of parallelization, preconcentration, or miniaturization, it opens up exciting opportunities for the development of ultra-sensitive digital assay in a format that is compatible for point-of-care.