If I create a view, I can add a filter that filters on a relative value on some built-in date field, such as Post date. For instance, the screenshot below shows a filter I've created that will show articles posted in the last four days.
Unfortunately, there is no date field type in core. To get a date field type, you can install the Date module. This allows you to create nice widgets for inputting dates. However, I've found no way to filter the date fields created by the date module by a relative value (like the filter shown above for Post date). There are
Is equal to and
Is not equal to operators, but no greater than operator, in the "Configure filter criterion" screen.
I believe that this should be possible, as is also evident from Nigel Waters's upvoted answer to this question: view to show content with future date. However, the exact steps one must take to reproduce the result shown in the upvoted answer eludes me.