Your systematic review can be documented using the PRISMA Flow Diagram:
The PRISMA flow diagram visually summarises the screening process. It initially records the number of articles found and then makes the selection process transparent by reporting on decisions made at various stages of the systematic review. Numbers of articles are recorded at the different stages. When you're excluding articles at the full-text stage, it is important to include the reasons for exclusion.

Specialised software can assist when screening results. Records (which may be from an EndNote or Mendeley library) can be imported directly into these programs.

Covidence is an online systematic review program developed by, and for, systematic reviewers. It can import citations from reference managers like EndNote, facilitate the screening of abstracts and full-text, populate risk of bias tables, assist with data extraction, and export to all common formats.
Covidence is a core component of Cochrane's review production toolkit and has recently also been endorsed by JBI.
Which version of Covidence is best for you?

The Systematic Review Toolbox is a community-driven, searchable, web-based catalogue of tools that support various tasks within the systematic review and wider evidence synthesis process.
The toolbox aims to help researchers and reviewers find the following:
Users can perform a simple keyword (i.e. Quick) search to locate tools, or a more detailed (i.e. Advanced) search allowing users to select various criteria to find specific types of tools.

Rayyan is a free web application to help systematic review authors create systematic reviews, collaborate on them, maintain them over time and get suggestions for article inclusion.

DistillerSR is an online application designed specifically for the screening and data extraction phases of a systematic review. Subscription Fee. Additional technical information at: http://www.tectutorials.com/TERDistillerSR.html
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Once you have completed your searches and used a reference manager (such as EndNote or Mendeley) to export your results, you can then begin screening your results. Screening can be done using EndNote or you can use a screening tool eg Covidence (your references can be exported from EndNote to Covidence).
You can commence the selection of relevant studies based on the inclusion and exclusion criteria. This process is usually done by 2-3 independent reviewers so as to control selection bias and minimise the risk of excluding any relevant studies. When there is disagreement between reviewers then discussion can occur to decide outcomes.
Remove duplicate records from your results
Examine titles and abstracts to exclude articles that don't meet the inclusion criteria
Find the full text of relevant articles
Keep together any reports referring to the same study
Screen full-text articles against criteria for inclusion
Make any final decisions on study inclusion