Platforms that offer massively parallel, label-free biosensing can, in principle, be created by combining all-electrical detection with low-cost integrated circuits. Examples include field-effect transistor arrays, which are used for mapping neuronal signals(1,2) and sequencing DNA(3,4). Despite these successes, however, bioelectronics has so far failed to deliver a broadly applicable biosensing platform. This is due, in part, to the fact that d.c. or low-frequency signals cannot be used to probe beyond the electrical double layer formed by screening salt ions(5-8), which means that under physiological conditions the sensing of a target analyte located even a short distance from the sensor (similar to 1 nm) is severely hampered. Here, we show that high-frequency impedance spectroscopy can be used to detect and image microparticles and living cells under physiological salt conditions. Our assay employs a large-scale, high-density array of nanoelectrodes integrated with CMOS electronics on a single chip and the sensor response depends on the electrical properties of the analyte, allowing impedance-based fingerprinting. With our platform, we image the dynamic attachment and micromotion of BEAS, THP1 and MCF7 cancer cell lines in real time at submicrometre resolution in growth medium, demonstrating the potential of the platform for label/tracer-free high-throughput screening of anti-tumour drug candidates.