Recording a THz waveform in single-shot is needed in Time-Domain Spectroscopy (TDS) and the study of accelerator physics. However, existing methods suffer from fundamental trade-offs in bandwidth, resolution, and sensitivity, which have limited their applications so far. We present here a new method for single-shot Time-Domain Spectrometers - or equivalently terahertz Analog to Digital Converters (ADC) - that can be operated with unprecedented temporal resolution and bandwidths. The core of the method consists of a novel association of classical THz electro-optic detection, together with the theoretical concept known as diversity, borrowed from photonic time-stretch. We present prototypes and tests of two single-shot systems: a TDS system capable of single-shot THz spectroscopy with record spectral resolution, and a THz recorder that records the electric field created by 200 fs long relativistic electron bunches at European XFEL.