This thesis develops and applies the nanopore tool to probe chemical structures and physical processes at the single-molecule level: from single ions to DNA molecules. Nanopore experiments electrically measure the ionic transport through the pore and its modulation from the local environment which can be caused by translocations of an analyte such as objects like DNA molecules or change of the physical conditions such as surface charge. Its precision relies on the physical dimension of the nanopore probe. In this thesis, the atom by atom engineering of single-layer molybdenum disulfide (MoS2) nanopores was achieved using transmission electron microscopy (TEM) or controlled electrochemical reaction (ECR), which further enabled the following investigations. On the translational side, the key driver of the application of nanopores is single molecule DNA sequencing. The sequence of DNA can be extracted based on the modulation of ionic current through the pore by individual nucleotides. To this end, we realized for the first time with solid-state nanopores, identification of all four types of nucleotides by introducing an ionic liquid based viscosity gradient system to control the translocation dynamics. This method provides a potential route for sequencing with solid-state nanopores. On the fundamental side, nanopore experiments could probe physics of single ion transport and with subnanometer pores, we discovered Coulomb blockade for the first time in ionic transport, as the counterpart of quantum dots, and proposed a new mesoscopic understanding for biological ion channel transport. From an engineering perspective, measurement with a single nanopore can avoid averaging over many pores and allow accurately identifying individual parameters for membrane-based processes. With single-layer MoS2 nanopores, we realized the first exploration of a two-dimensional (2D) membrane for osmotic power generation. This thesis demonstrates that nanoscopic, atomically thin pores allow for the exploration of applications in DNA sequencing and investigations of fundamental ion transport for biological ion channels and membrane-based processes.