Abstract: Generative Artificial Intelligence (GAI) has recently achieved significant success, enabling anyone to create texts, images, videos, and even computer codes while providing insights that might not be possible with traditional tools. To stimulate future research, this work provides a brief summary of the ongoing and historical developments in GAI over the past 70 years. The achievements are grouped into four categories: (i) rule-based generative systems that follow specialized rules and instructions, (ii) model-based generative algorithms that produce new content based on statistical or graphical models, (iii) deep generative methodologies that utilize deep neural networks to learn how to generate new content from data, and (iv) foundation models that are trained on extensive datasets and capable of performing a variety of generative tasks. This paper also reviews successful generative applications and identifies open challenges posed by remaining issues. In addition, this paper describes potential research directions aimed at better utilizing, understanding, and harnessing GAI technologies.