The paper provides a comprehensive treatment of time-mode noise-shaping analog-to-digital converters (ADCs). An in-depth examination of the principle, advantages, and challenges of VCO quantizers is provided. Open-loop techniques that combat the nonlinear voltage-to-phase characteristics of VCO quantizers are investigated and the limitations are studied. The performance of open-loop time-mode ADCs is also compared. The intrinsic advantages and limitations of closed-loop configurations of time-mode noise-shaping ADCs are explored. It is followed by an detailed investigation of closed-loop time-mode noise-shaping ADCs with an emphasis on techniques combating the effect of the nonlinear voltage-to-phase characteristics of VCO quantizers and the effect of the nonlinearity of internal DACs. The performance of reported closed-loop time-mode noise-shaping ADCs is compared.