Deep Learning methods such as Deep Representation Learning (DRL) and, specifically, the Variational Autoencoder (VAE), have been widely used to handle the high dimensionality of available datasets. Hence, these methods have been applied to study cancer through omics data. Cancer is one of the leading causes of death worldwide, and its complex and dynamic nature makes it especially difficult to study. However, the temporal dimension of cancer progression is a target that has not been tackled. In this systematic literature review, we explore the use of DRL, particularly the VAE, in cancer studies with omics data in a temporal context. Our research reveals that the most common uses of the VAE in cancer studies are related to subtyping, diagnosis, and prognosis. Meanwhile, cancer\'s temporal aspect is often overlooked, namely, because of the lack of longitudinal data. We propose that applying the VAE as a generative model to study cancer in time, for example, focusing on cancer staging, will lead to meaningful advancements in our understanding of cancer.