Globalization provides several opportunities to companies, including access to multiple markets, new revenues, knowledge and technologies, that increases their competitivity. On the other hand, it generates a series of threats within an environment of worldwide growing instability, originated from social and geopolitical conflicts, together with financial and economical risks. Moreover, the solidification of an unstable global economical system is at the heart of such conflicts and risks. Such aspects of the Globalization process, both the positive and negative ones, may cause aggressive disturbances and oscillations in the markets creating challenges to the global corporate strategic management. The modern approaches to managerial globalization process take into account both these aspects, opportunities and threats, however in an unordered way. In this work we present a qualitative analysis of the main approaches to global companies, aiming to pinpoint the challenges of corporate management of companies under globalization. Moreover, we demonstrate that a search for alternatives to a company's survival and domestic independence requires a change of perspective regarding their administrative functions and the formulation and implementation of their strategies, in order to define the necessary infrastructure to allow its business growth. It is also shown that a search for new markets requires several dynamic abilities but also a systematic method to manage internal and external challenges.