Several companies have recently developed small and intermediate-scale quantum computing devices. These systems lack the size and accuracy required for error correction, which would seem to be necessary for practical applications. However there is now a tremendous hope--and hype--for the possibility of finding near-term applications that do not require the overhead required for full error correction. In this talk I will review the current state of the field and discuss these recent developments. I will also discuss our own approach, called the single-excitation subspace method, to this challenge.