Disclosed are solid-state nanopore devices having pores of nanometer-scale thickness, which ultrathin (e.g., less than 10 nm thick) pores enable devices having improved resolution. Also provided are methods of fabricating such devices and of using such devices. The invention also provides nanometer-thick membranes and related methods of fabricating such membranes, which membranes are useful in high resolution microscopy applications. Further disclosed are devices for detection of analytes—including miRNA—that may be small in size and may also be present in only small quantities.