Nanopore-based sensors typically work by monitoring transient pulses in conductance via current-time traces as molecules translocate through the nanopore. The unique property of being able to monitor single molecules gives nanopore sensors the potential as quantitative sensors based on the counting of single molecules. This review provides an overview of the concepts and fabrication of nanopore sensors as well as nanopore sensing with a view toward using nanopore sensors for quantitative analysis. We first introduce the classification of nanopores and highlight their applications in molecular identification with some pioneering studies. The review then shifts focus to recent strategies to extend nanopore sensors to devices that can rapidly and accurately quantify the amount of an analyte of interest. Finally, future prospects are provided and briefly discussed. The aim of this review is to aid in understanding recent advances, challenges, and prospects for nanopore sensors for quantitative analysis.