Along with more prevalent solid-state nanopores, glass or quartz nanopipettes have found applications in resistive-pulse and rectification sensing. Their advantages include the ease of fabrication, small physical size and needle-like geometry, rendering them useful for local measurements in small spaces and delivery of nanoparticles/biomolecules. Carbon nanopipettes fabricated by depositing a thin carbon layer on the inner wall of a quartz pipette provide additional means for detecting electroactive species and fine-tuning the current rectification properties. In this paper, we discuss the fundamentals of resistivepulse sensing with nanopipettes and our recent studies of current rectification in carbon pipettes.