Custom Twitter widgets


I’m having a bit of trouble finding any resources about making a custom Twitter widget for a site.

Basically, I want to create a real time twitter feed to implement within a site, that automatically updates every few seconds to show new tweets.

I know this used to be possible, but it seems like Twitter just wants me to use their default widget these days instead of my own solution.

Does anyone have any tips / links to good resources?

Thanks in advance!