PARIS--Apple’s tax bill is just the beginning.

The European Union’s decision Tuesday that Apple Inc. owes roughly €13 billion ($14.5 billion) in what it calls uncollected taxes over a decade, represents a new high-water mark in the bloc’s efforts to rein in alleged excesses of American tech giants.

But it is also just the first shot in what is expected to be a busy autumn for European officials, who are pushing forward a raft of regulations and investigations aimed at altering the behavior of a cadre of U.S.-based internet superpowers. The moves are being taken by a host of players—from EU regulators in Brussels to a bevy of national authorities across the continent. They are targeting areas ranging from personal privacy to anti-competition issues.

In coming weeks, EU bodies plan to debate new telecom rules that could expand to cover services like WhatsApp, proposed legislation to push news aggregators to pay newspapers for showing snippets of content, and potential audiovisual rules that would force companies like Netflix Inc. to finance European movies.

At the same time, authorities in capitals like Brussels, Paris and Berlin are pursuing investigations involving big companies like Alphabet Inc.’s Google, Amazon.com Inc. and Facebook Inc., related to alleged tax avoidance, anticompetitive behavior and privacy concerns.