Dynamic DNA nanodevices represent powerful tools for the interrogation and manipulation of biological systems. Yet, implementation remains challenging due to nuclease degradation and other cellular factors. Use of l-DNA, the nuclease resistant enantiomer of native d-DNA, provides a promising solution. On this basis, we recently developed a strand displacement methodology, referred to as ‘heterochiral’ strand displacement, that enables robust l-DNA nanodevices to be sequence-specifically interfaced with endogenous d-nucleic acids. However, the underlying reaction – strand displacement from PNA–DNA heteroduplexes – remains poorly characterized, limiting design capabilities. Herein, we characterize the kinetics of strand displacement from PNA–DNA heteroduplexes and show that reaction rates can be predictably tuned based on several common design parameters, including toehold length and mismatches. Moreover, we investigate the impact of nucleic acid stereochemistry on reaction kinetics and thermodynamics, revealing important insights into the biophysical mechanisms of heterochiral strand displacement. Importantly, we show that strand displacement from PNA–DNA heteroduplexes is compatible with RNA inputs, the most common nucleic acid target for intracellular applications. Overall, this work greatly improves the understanding of heterochiral strand displacement reactions and will be useful in the rational design and optimization of l-DNA nanodevices that operate at the interface with biology.