The use of ferroelectric negative capacitance (NC) is suggested to be an appealing contender to reduce the subthreshold swing of field-effect transistors and thus the power dissipation in integrated logic circuits. Ferroelectric thin films based on HfO₂ and ZrO₂ are most promising for such applications due to their scalability and compatibility with current integration processes. To assess this potential, it is important to distinguish various reported NC effects, which can have rather different physical origins. While transient NC effects during polarization switching are often reported and are accompanied by a hysteresis, stabilized NC in HfO₂- and ZrO₂-based ferroelectrics without hysteresis is still controversially discussed. Here, we review the experimental reports on NC in these ferroelectric materials and discuss their significance concerning applications. Overall, it is concluded that stabilized NC in HfO₂- and ZrO₂-based ferroelectrics has yet to be demonstrated unambiguously, although recent works have reported promising results.