Messenger RNA (mRNA) and long noncoding RNA (lncRNA) can be subjected to a variety of post-transcriptional modifications that markedly influence their fate and function. This concept of 'epitranscriptomic' modifications and the understanding of their function has been driven by new technologies for transcriptome-wide mapping of modified nucleotides using next-generation sequencing. Mapping technologies have successfully documented the location and prevalence of several modified nucleotides in the transcriptome. However, some mapping methods have led to proposals of pervasive novel RNA modifications that have subsequently been shown to be exceptionally rare. These controversies have resulted in confusion about the identity of the modified nucleotides comprising the epitranscriptome in mRNA and lncRNA. Here we discuss the different transcriptome-wide technologies for mapping modified nucleotides. We describe why these methods can have poor accuracy and specificity. Finally, we describe emerging strategies that minimize false positives and other pitfalls associated with mapping and measuring epitranscriptomic modifications.