Background. The quantification of subtle patterns in sequential data, and their changes, has considerable potential utility throughout cardiology, including the analysis of heart rate rhythms. Aim of the study. Approximate entropy (ApEn), a recently developed statistic quantifying serial irregularity, has been applied in numerous studies throughout mathematics and applications, especially biology. We indicate results to date, and future direction, of interest to cardiologists. Methods. We define ApEn, indicating basic properties. We discuss typical applications of ApEn, with special focus on a representative aspect of ApEn applications to heart rate dynamics, to pre- and early life studies. Subsequently, we introduce and briefly discuss cross-ApEn, a thematically similar quantification of two-variable asynchrony. Results. ApEn consistently detects subtle shifts in heart rate rhythmicity in many studies in which mean levels and classical variability assessments fail to discriminate normative from pathophysiological subjects. Greater regularity (lower ApEn) clinically corresponds to compromised physiology in all cardiologic settings discussed herein. We provide a mechanistic interpretation of lowered ApEn values, based on mathematical analysis, yet linked to physiology. We discuss and clarify why ApEn is complementary to classical ‘moment analysis’, to chaos-related statistical measures, and to spectral and correlation measures, and oftentimes provides clearer discriminatory capability. Conclusions. Both ApEn and cross-ApEn have significant potential to consequentially enhance present statistical methodologies of analysis of cardiologic data, in both clinical and in research settings.