Nanophotonic device building blocks, such as optical nano/microcavities and plasmonic nanostructures, lie at the forefront of sensing and spectrometry of trace biological and chemical substances. A new class of nanophotonic architecture has emerged by combining optically resonant dielectric nano/microcavities with plasmonically resonant metal nanostructures to enable detection at the nanoscale with extraordinary sensitivity. Initial demonstrations include single-molecule detection and even single-ion sensing. The coupled photonic-plasmonic resonator system promises a leap forward in the nanoscale analysis of physical, chemical, and biological entities. These optoplasmonic sensor structures could be the centrepiece of miniaturised analytical laboratories, on a chip, with detection capabilities that are beyond the current state of the art. In this paper, we review this burgeoning field of optoplasmonic biosensors. We first focus on the state of the art in nanoplasmonic sensor structures, high quality factor optical microcavities, and photonic crystals separately before proceeding to an outline of the most recent advances in hybrid sensor systems. We discuss the physics of this modality in brief and each of its underlying parts, then the prospects as well as challenges when integrating dielectric nano/microcavities with metal nanostructures. In Section 5, we hint to possible future applications of optoplasmonic sensing platforms which offer many degrees of freedom towards biomedical diagnostics at the level of single molecules.