Digital contact tracing (DCT) applications have been introduced in many countries to aid the containment of COVID-19 outbreaks. Initially, enthusiasm was high regarding their implementation as a non-pharmaceutical intervention (NPI). However, no country was able to prevent larger outbreaks without falling back to harsher NPIs. Here, we discuss results of a stochastic infectious-disease model that provide insights in how the progression of an outbreak and key parameters such as detection probability, app participation and its distribution, as well as engagement of users impact DCT efficacy informed by results of empirical studies. We further show how contact heterogeneity and local contact clustering impact the intervention’s efficacy. We conclude that DCT apps might have prevented cases on the order of single-digit percentages during single outbreaks for empirically plausible ranges of parameters, ignoring that a substantial part of these contacts would have been identified by manual contact tracing. This result is generally robust against changes in network topology with exceptions for homogeneous-degree, locally-clustered contact networks, on which the intervention prevents more infections. An improvement of efficacy is similarly observed when app participation is highly clustered. We find that DCT typically averts more cases during the super-critical phase of an epidemic when case counts are rising and the measured efficacy therefore depends on the time of evaluation.