Solution-based single-molecule fluorescence spectroscopy is a powerful experimental tool with applications in cell biology, biochemistry and biophysics. The basic feature of this technique is to excite and collect light from a very small volume and work in a low concentration regime resulting in rare burst-like events corresponding to the transit of a single molecule. Detecting photon bursts is a challenging task: the small number of emitted photons in each burst calls for high detector sensitivity. Bursts are very brief, requiring detectors with fast response time and capable of sustaining high count rates. Finally, many bursts need to be accumulated to achieve proper statistical accuracy, resulting in long measurement time unless parallelization strategies are implemented to speed up data acquisition. In this paper we will show that silicon single-photon avalanche diodes (SPADs) best meet the needs of single-molecule detection. We will review the key SPAD parameters and highlight the issues to be addressed in their design, fabrication and operation. After surveying the state-of-the-art SPAD technologies, we will describe our recent progress towards increasing the throughput of single-molecule fluorescence spectroscopy in solution using parallel arrays of SPADs. The potential of this approach is illustrated with single-molecule Förster resonance energy transfer measurements.