Cross-filtering
In a chart's Setup, tick Apply cross-filtering. Clicking a bar or table row then filters every other chart on the page to that value.
It is the fastest way to make a static report feel like a tool — click East on the region chart and the whole page becomes an East report. Clicking again clears it.
Enable it on your main dimension charts, not on everything. A page where every component filters every other is disorienting.
Drill-down
In Setup, turn on Drill down and add several dimensions in order — Country, then Region, then City.
The reader gets arrows to move up and down the hierarchy inside one chart. That replaces three charts with one, which is usually a better use of the space.
Chart interactions
Beyond cross-filtering, components can be given actions: a button linking to another page, a chart element opening a URL with the clicked value passed in.
Multi-page reports with navigation buttons in the header work well — an overview page with drill-through to detail pages, rather than one enormous page.
How much is too much
Every interactive element is something the reader has to understand. A report with two well-chosen controls and cross-filtering on one chart gets used. A report with nine controls, drill-down everywhere and cross-filtering on everything gets abandoned.
Start from the two or three questions the audience actually asks, and make those easy.