Background: Digitized histopathological tissue slides and genomics profiling data are available for many patients with solid tumors. In the last 5 years, Deep Learning (DL) has been broadly used to extract clinically actionable information and biological knowledge from pathology slides and genomic data in cancer. In addition, a number of recent studies have introduced multimodal DL models designed to simultaneously process both images from pathology slides and genomic data as inputs. By comparing patterns from one data modality with those in another, multimodal DL models are capable of achieving higher performance compared to their unimodal counterparts. However, the application of these methodologies across various tumor entities and clinical scenarios lacks consistency. Methods: Here, we present a systematic survey of the academic literature from 2010 to November 2023, aiming to quantify the application of DL for pathology, genomics, and the combined use of both data types. After filtering 3048 publications, our search identified 534 relevant articles which then were evaluated by basic (diagnosis, grading, subtyping) and advanced (mutation, drug response and survival prediction) application types, publication year and addressed cancer tissue. Results: Our analysis reveals a predominant application of DL in pathology compared to genomics. However, there is a notable surge in DL incorporation within both domains. Furthermore, while DL applied to pathology primarily targets the identification of histology-specific patterns in individual tissues, DL in genomics is more commonly used in a pan-cancer context. Multimodal DL, on the contrary, remains a niche topic, evidenced by a limited number of publications, primarily focusing on prognosis predictions. Conclusion: In summary, our quantitative analysis indicates that DL not only has a well-established role in histopathology but is also being successfully integrated into both genomic and multimodal applications. In addition, there is considerable potential in multimodal DL for harnessing further advanced tasks, such as predicting drug response. Nevertheless, this review also underlines the need for further research to bridge the existing gaps in these fields.