Measuring physical quantities in the nanometric region inside single cells is of great importance for understanding cellular activity. Thus, the development of biocompatible, sensitive, and reliable nanobiosensors is essential for progress in biological research. Diamond nanoparticles containing nitrogen-vacancy centers (NVCs), referred to as fluorescent nanodiamonds (FNDs), have recently emerged as the sensors that show great promise for ultrasensitive nanosensing of physical quantities. FNDs emit stable fluorescence without photobleaching. Additionally, their distinctive magneto-optical properties enable an optical readout of the quantum states of the electron spin in NVC under ambient conditions. These properties enable the quantitative sensing of physical parameters (temperature, magnetic field, electric field, pH, etc.) in the vicinity of an FND; hence, FNDs are often described as "quantum sensors". In this review, recent advancements in biosensing applications of FNDs are summarized. First, the principles of orientation and temperature sensing using FND quantum sensors are explained. Next, we introduce surface coating techniques indispensable for controlling the physicochemical properties of FNDs. The achievements of practical biological sensing using surface-coated FNDs, including orientation, temperature, and thermal conductivity, are then highlighted. Finally, the advantages, challenges, and perspectives of the quantum sensing of FND are discussed. This review article is an extended version of the Japanese article, In Situ