Malware detection has become a major concern due to the increasing number and complexity of malware. Traditional detection methods based on signatures and heuristics are used for malware detection, but unfortunately, they suffer from poor generalization to unknown attacks and can be easily circumvented using obfuscation techniques. In recent years, Machine Learning (ML) and notably Deep Learning (DL) achieved impressive results in malware detection by learning useful representations from data and have become a solution preferred over traditional methods. More recently, the application of such techniques on graph-structured data has achieved state-of-the-art performance in various domains and demonstrates promising results in learning more robust representations from malware. Yet, no literature review focusing on graph-based deep learning for malware detection exists. In this survey, we provide an in-depth literature review to summarize and unify existing works under the common approaches and architectures. We notably demonstrate that Graph Neural Networks (GNNs) reach competitive results in learning robust embeddings from malware represented as expressive graph structures, leading to an efficient detection by downstream classifiers. This paper also reviews adversarial attacks that are utilized to fool graph-based detection methods. Challenges and future research directions are discussed at the end of the paper. CCS Concepts: • General and reference → Surveys and overviews; • Security and privacy → Malware and its mitigation; • Computing methodologies → Learning latent representations; Neural networks; Spectral methods.