Recent advances in single-cell genomics provide an alternative to largely gene-centric metagenomics studies, enabling whole-genome sequencing of uncultivated bacteria. However, single-cell assembly projects are challenging due to (i) the highly nonuniform read coverage and (ii) a greatly elevated number of chimeric reads and read pairs. While recently developed single-cell assemblers have addressed the former challenge, methods for assembling highly chimeric reads remain poorly explored. We present algorithms for identifying chimeric edges and resolving complex bulges in de Bruijn graphs, which significantly improve single-cell assemblies. We further describe applications of the single-cell assembler SPAdes to a new approach for capturing and sequencing "microbial dark matter" that forms small pools of randomly selected single cells (called a mini-metagenome) and further sequences all genomes from the mini-metagenome at once. On single-cell bacterial datasets, SPAdes improves on the recently developed E+V-SC and IDBA-UD assemblers specifically designed for single-cell sequencing. For standard (cultivated monostrain) datasets, SPAdes also improves on A5, ABySS, CLC, EULER-SR, Ray, SOAPdenovo, and Velvet. Thus, recently developed single-cell assemblers not only enable single-cell sequencing, but also improve on conventional assemblers on their own turf. SPAdes is available for free online download under a GPLv2 license.