Natural monopolies in the technology industry have been the subject of much debate lately. This paper addresses the topic of natural monopolies in the technology industry, with an emphasis on Google. In order to gain a better insight into the overall market situation, a historical introduction to competition issues was first made. Comparing the laws in the EU and the US, a comparative analysis of both systems was made. Emphasis is placed on the Sherman Act in the US and Articles 101. and 102. of the Treaty on the Functioning of the EU. A study of the business of Google has made an analysis of whether the said company is abusing its dominance in the markets of search engines and mobile operating systems. This hypothesis was confirmed and supported by examples of contracts that the company signs with manufacturers in the market. The last chapter examines previous cases of stopping monopoly in the United States, and the analysis conducted could in the same way halt the dominance of Google. The hypothesis of breaking up a company to increase competition in the search engine and mobile operating market was rejected due to the fact that there was no concrete evidence to support the thesis that such a remedy would manage to provide a better market for competitors and consumers.