There are two main ways to discover or design small drug molecules. The first involves fine-tuning existing molecules or commercially successful drugs through quantitative structure-activity relationships and virtual screening. The second approach involves generating new molecules through de novo drug design or inverse quantitative structure-activity relationship. Both methods aim to get a drug molecule with the best pharmacokinetic and pharmacodynamic profiles. However, bringing a new drug to market is an expensive and time-consuming endeavor, with the average cost being estimated at around $2.5 billion. One of the biggest challenges is screening the vast number of potential drug candidates to find one that is both safe and effective. The development of artificial intelligence in recent years has been phenomenal, ushering in a revolution in many fields. The field of pharmaceutical sciences has also significantly benefited from multiple applications of artificial intelligence, especially drug discovery projects. Artificial intelligence models are finding use in molecular property prediction, molecule generation, virtual screening, synthesis planning, repurposing, among others. Lately, generative artificial intelligence has gained popularity across domains for its ability to generate entirely new data, such as images, sentences, audios, videos, novel chemical molecules, etc. Generative artificial intelligence has also delivered promising results in drug discovery and development. This review article delves into the fundamentals and framework of various generative artificial intelligence models in the context of drug discovery via de novo drug design approach. Various basic and advanced models have been discussed, along with their recent applications. The review also explores recent examples and advances in the generative artificial intelligence approach, as well as the challenges and ongoing efforts to fully harness the potential of generative artificial intelligence in generating novel drug molecules in a faster and more affordable manner. Some clinical-level assets generated form generative artificial intelligence have also been discussed in this review to show the ever-increasing application of artificial intelligence in drug discovery through commercial partnerships.