Continual learning (CL) is a major challenge of machine learning (ML) and describes the ability to learn several tasks sequentially without catastrophic forgetting (CF). Recent works indicate that CL is a complex topic, even more so when real-world scenarios with multiple constraints are involved. Several solution classes have been proposed, of which so-called replay-based approaches seem very promising due to their simplicity and robustness. Such approaches store a subset of past samples in a dedicated memory for later processing: while this does not solve all problems, good results have been obtained. In this article, we empirically investigate replay-based approaches of continual learning and assess their potential for applications. Selected recent approaches as well as own proposals are compared on a common set of benchmarks, with a particular focus on assessing the performance of different sample selection strategies. We find that the impact of sample selection increases when a smaller number of samples is stored. Nevertheless, performance varies strongly between different replay approaches. Surprisingly, we find that the most naive rehearsal-based approaches that we propose here can outperform recent state-of-the-art methods.