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In this paper, we introduce FRETBursts, an open source software  for analysis of freely-diffusing smFRET data.  Fundamental steps in the analysis involve identifying photon bursts  from single molecules in a continuous stream of photons, estimating  background and other correction factors, filtering bursts and extracting  the corrected FRET efficiencies for each sub-population. FRETBursts allows executing all these the fundamental  steps of smFRET bursts  analysis  usingboth  state-of-the-art algorithms and improved techniques.  FRETBursts provides as well as novel techniques,  while providing  an open, robust and well-documented implementation for commonly employed algorithms and implementation.  Therefore FRETBursts  represents an ideal platform for comparison and development of new methods in burst analysis. We employ modern software engineering principles in order to  minimizethe chance of  bugs and facilitate long-term maintainability. Furthermore, we place a strong focus on reproducibility by relying on  Jupyter notebooks forthe execution of  FRETBursts workflows. execution.  Notebooks are executable documents capturing all the steps of the  analysis (including data files, input parameters, and results) and can  be easily shared to replicate complete smFRET analyses.  This execution model allows Notebooks allow  beginners to execute complex workflows and advanced users to customize the analysis for their own needs.  By unifying bundling in a single document  analysis description, code and results in a single document, results,  FRETBursts allows to  seamless sharing of workflows, share analysis workflows  and results,  encourages reproducibility and facilitates collaboration among researchers  in the single-molecule community and beyond. community.