Heart rate variability (HRV) is the variation of cardiac inter-beat intervals over time resulting largely from the interplay between the sympathetic and parasympathetic branches of the autonomic nervous system. Individual differences in HRV are associated with emotion regulation, personality, psychopathology, cardiovascular health, and mortality. Previous studies have shown significant heritability of HRV measures. Here we extend genetic research on HRV by investigating sex differences in genetic underpinnings of HRV, the degree of genetic overlap among different measurement domains of HRV, and phenotypic and genetic relationships between HRV and the resting heart rate (HR). We performed electrocardiogram (ECG) recordings in a large population-representative sample of young adult twins (n=1060 individuals) and computed HRV measures from three domains: time, frequency, and nonlinear dynamics. Genetic and environmental influences on HRV measures were estimated using linear structural equation modeling of twin data. The results showed that variability of HRV and HR measures can be accounted for by additive genetic and non-shared environmental influences (AE model), with no evidence for significant shared environmental effects. Heritability estimates ranged from 47 to 64%, with little difference across HRV measurement domains. Genetic influences did not differ between genders for most variables except the square root of the mean squared differences between successive R-R intervals (RMSSD, higher heritability in males) and the ratio of low to high frequency power (LF/HF, distinct genetic factors operating in males and females). The results indicate high phenotypic and especially genetic correlations between HRV measures from different domains, suggesting that >90% of genetic influences are shared across measures. Finally, about 40% of genetic variance in HRV was shared with HR. In conclusion, both HR and HRV measures are highly heritable traits in the general population of young adults, with high degree of genetic overlap across different measurement domains.