twarc is a command line tool and Python library for archiving Twitter data. It has a number of features and filter options and good documentation (https://twarc-project.readthedocs.io/en/latest/). Note that the data is stored as line-oriented JSON. twarc was developed as part of the Documenting the Now project. twarc has been updated to work with the Twitter v2 API and Academic Access.

Hydrator is a desktop application created by the Documenting the Now project. It is used to reconstitute Twitter datasets using tweet identifiers. Since Twitter's Terms of Service do not allow the full JSON for datasets of tweets to be distributed to third parties, tools like Hydrator helps turn these tweet IDs back into JSON.

rtweet is a Twitter client using R. The R community is very robust, so there are a number of tutorials online for using rtweet (and a documentation website: http://rtweet.info/). The advantage of using rtweet is that it brings your Twitter data into R, where you can readily clean, subset, analyze, and graph your data. The downside is that it's not set up for systematically gathering and saving tweets.

An R package for using the Academic Research API. Lots of great options for filtering searches.

Social Feed Manager is open source software created by the George Washington University Libraries to support gathering and archiving social media and websites. Social Feed Manager can collect data from Twitter, Weibo, Tumblr, and Flickr.

FireAnt is software that can collect Twitter data as well as work with pre-existing data sets (in JSON, CSV, TSV, XLSX formats). Can be used to create timeseries graphs, network data, and maps (based on latitude and longitude).

Really, it's a template for using Google Sheets, but TAGS is a useful, free way to collect tweets directly into a spreadsheet.

NodeXL is a plug-in for Microsoft Excel that is primarily designed to create network graphs. The social media/Twitter functionality is limited to the NodeXL Pro license, but in addition to network analysis and graphing, you can also do sentiment analysis and other text-related things.

A plugin for Gephi (open source network analysis software) that allows you to collect tweets in real time and either visualize networks directly in Gephi or export the tweets to Excel.

You can use NCapture to get Twitter data and then import from there into NVivo for analysis. NVivo supports cluster and network analysis, mapping, or you can view tweets for coding.

A Python-based tool created specifically for working with social media text.

An R package for doing text analysis using tidy data principles, including sentiment analysis.

FireAnt is software that can collect Twitter data as well as work with pre-existing data sets (in JSON, CSV, TSV, XLSX formats). Can be used to create timeseries graphs, network data, and maps (based on latitude and longitude).