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The European Union's Horizon 2020 research program is funding a project to research cybercriminality and design methods to prevent, investigate, and mitigate cybercriminal behavior, including adversarial machine learning attacks (AMLAs). AMLAs are cyber-attacks that target machine learning systems, impairing their functioning or obtaining unauthorized information. The EU's current legal framework sets out offenses that could cover AMLAs, and the upcoming EU AI Regulation is expected to boost the resilience of ML systems to such attacks. However, there is a need for clarity on the scope of application of criminal offenses and potential legislative and institutional reform. AMLAs can cause significant harm to users, developers, and public trust in AI/ML systems, and can be driven by various intentions, including competitive advantage, hacker satisfaction, and cyberwarfare goals. The legal regulation of AMLAs is a relatively new topic, and there are several legal and regulatory challenges, including the scope of criminal offenses, prevention, and response to AMLAs.