Modern advances in sequencing technologies have enabled exploration of molecular biology at unprecedented scale and resolution. Transcriptome sequencing (RNA-seq), in particular, has been widely adopted as a routine cost-effective method for assaying both genetic and functional characteristics of biological systems with resolution down to individual cells. Clinical research and applications leveraging these technologies have largely targeted tumor biology, where transcriptome sequencing can capture tumor genetic and epigenetic characteristics and aid with understanding the etiology or guide treatments. Specialized computational methods and bioinformatic software tools are essential for processing and analyzing RNA-seq to explore various aspects of tumor biology including driver mutations, genome rearrangements, and aneuploidy. With single cell resolution, such methods can yield insights into tumor cellular composition and heterogeneity. Here, we developed methods and tools to support cancer transcriptome studies for bulk and single cell tumor transcriptomes, focusing primarily on fusion transcript detection and predicting large-scale copy number alternations from RNA-seq. These efforts culminated in the development of STAR-Fusion for fast and accurate detection of fusion transcripts, FusionInspector for further characterizing predicted fusion transcripts and discriminating likely artifacts, and TrinityFusion for de novo reconstruction of fusion transcripts and tumor viruses. We also developed advanced methods for predicting copy number alterations and subclonal architecture from tumor and normal single cell RNA-seq data, as incorporated into our InferCNV software. In addition to these bioinformatic method and software developments, we applied our fusion detection methods to thousands of tumor and normal samples and gain novel insights that should further help guide researchers with clinical applications of fusion transcript discovery.