Google has a history of getting in trouble with authorities over allegations of anti-competitive and monopolistic practices. In almost every instance thus far, they have had some way to defend themselves in court. Their current antitrust woes in the EU, headed by Margarethe Vestager, may land them in roughly 3 billion euros' worth of trouble. While the official charges in the most recent spat have only recently been issued, this is an issue that has followed Google from place to place over the years due in part to their size and the large number of different services they offer.
Google's biggest thus far of their monopoly and antitrust troubles, the current case in the EU, had its beginnings with a vertical search engine from the UK, called Foundem, back in 2006. Foundem, who had been doing somewhat well until then, was "penalized" by Google's algorithms and labeled as less relevant due to a lack of original content, being a search engine. This compounded when they suffered an AdWords penalty as well, by the same token, that caused their ad costs to skyrocket roughly one hundredfold. Google did eventually overturn both "algorithmic" penalties manually, resulting in a 10,000 percent jump in traffic for Foundem, but by then, the damage was done. During the intervening time, Foundem had gone to EU authorities to complain that Google was demoting them for anti-competitive reasons. They were joined by a number of other web outfits in time, which resulted in EU antitrust authorities eventually stepping in. Google and authorities tried to reach agreements and Google was constantly told to retool their solutions, whenever they did try to comply with regulators' wishes. Eventually, negotiations ended up falling through and bringing us to where we are today.
Unfortunately for Google, this may be an issue that they grapple with for the entirety of their existence and there a few reasons behind that. The first and biggest reason is Google's sheer scale and the number of areas they're in. Offering services in just about every market on the web, it's inevitable that Google would end up competing with everybody. Gathering results and data from all over the web at an alarming pace, even giving Google the benefit of the doubt on the antitrust issues, it's not hard to imagine their results ending up at least near the top due to their sheer relevance. This ties into another issue; Google sells search result sponsorships. While search engine optimization is a huge market, nothing can beat the advantage afforded by cold, hard cash. This model allows Google to sweep in more ad revenue as well; often, sites that pay to jump up in the ranks or end up on top as "Sponsored Results" often use Google's own ad platforms, AdSense and AdWords. The third big reason, to sum it up, is that Google often ends up sweeping new markets when they enter because of their size and technology. These factors mean Google may face down accusations of monopolistic practices forever.