Food insecurity comprises a major global public health threat, as its effects are detrimental to the mental, physical, and social aspects of the health and well-being of those experiencing it. We performed a narrative literature review on the magnitude of global food insecurity with a special emphasis on Greece and analyzed the major factors driving food insecurity, taking into consideration also the effect of the COVID-19 pandemic. An electronic search of international literature was conducted in three databases. More than 900 million people worldwide experience severe food insecurity, with future projections showing increasing trends. Within Europe, Eastern and Southern European countries display the highest food insecurity prevalence rates, with Greece reporting a prevalence of moderate or severe food insecurity ranging between 6.6% and 8% for the period 2019–2022. Climate change, war, armed conflicts and economic crises are major underlying drivers of food insecurity. Amidst these drivers, the COVID-19 pandemic had a profound impact on food insecurity levels around the globe, through halting economic growth, disrupting food supply chains and increasing unemployment and poverty. Tackling food insecurity through addressing its key drivers is essential to any progress towards succeeding the Sustainable Development Goal of “Zero Hunger”.