All-dielectric nanophotonics underpinned by the physics of bound states in the continuum (BICs) have demonstrated breakthrough applications in nanoscale light manipulation, frequency conversion and optical sensing. Leading BIC implementations range from isolated nanoantennas with localized electromagnetic fields to symmetry-protected metasurfaces with controllable resonance quality (Q) factors. However, they either require structured light illumination with complex beam-shaping optics or large, fabrication-intense arrays of polarization-sensitive unit cells, hindering tailored nanophotonic applications and on-chip integration. Here, we introduce radial quasi-bound states in the continuum (radial BICs) as a new class of radially distributed electromagnetic modes controlled by structural asymmetry in a ring of dielectric rod pair resonators. The radial BIC platform provides polarization-invariant and tunable high-Q resonances with strongly enhanced near fields in an ultracompact footprint as low as 2 µm2. We demonstrate radial BIC realizations in the visible for sensitive biomolecular detection and enhanced second-harmonic generation from monolayers of transition metal dichalcogenides, opening new perspectives for compact, spectrally selective, and polarization-invariant metadevices for multi-functional light-matter coupling, multiplexed sensing, and high-density on-chip photonics.