Accurate identification of bursting activity is an essential element in the characterization of neuronal network activity. Despite this, no one technique for identifying bursts in spike trains has been widely adopted. Instead, many methods have been developed for the analysis of bursting activity, often on an ad hoc basis. Here we provide an unbiased assessment of the effectiveness of eight of these methods at detecting bursts in a range of spike trains. We suggest a list of features that an ideal burst detection technique should possess and use synthetic data to assess each method in regard to these properties. We further employ each of the methods to reanalyze microelectrode array (MEA) recordings from mouse retinal ganglion cells and examine their coherence with bursts detected by a human observer. We show that several common burst detection techniques perform poorly at analyzing spike trains with a variety of properties. We identify four promising burst detection techniques, which are then applied to MEA recordings of networks of human induced pluripotent stem cell-derived neurons and used to describe the ontogeny of bursting activity in these networks over several months of development. We conclude that no current method can provide "perfect" burst detection results across a range of spike trains; however, two burst detection techniques, the MaxInterval and logISI methods, outperform compared with others. We provide recommendations for the robust analysis of bursting activity in experimental recordings using current techniques.