High-throughput RNA sequencing (RNA-seq) promises a comprehensive picture of the transcriptome, allowing for the complete annotation and quantification of all genes and their isoforms across samples. Realizing this promise requires increasingly complex computational methods. These computational challenges fall into three main categories: (i) read mapping, (ii) transcriptome reconstruction and (iii) expression quantification. Here we explain the major conceptual and practical challenges, and the general classes of solutions for each category. Finally, we highlight the interdependence between these categories and discuss the benefits for different biological applications.