Short answer
HubSpot's KB: use today's date and relative time in filters to segment, automate and report. On index pages, the Close date dropdown can be set to Today. Professional and Enterprise accounts can also create Time since and Time until calculation properties.
1. In HubSpot
The relevant screen in my demo portal.

2. Worth knowing
You rarely need a stored Today property; relative filters cover most cases.
3. Related
Lifecycle date properties and calculation properties.