Anomaly mining is an important problem that finds numerous applications in various real world do- mains such as environmental monitoring, cybersecurity, finance, healthcare and medicine, to name a few. In this article, I focus on two areas, (1) point-cloud and (2) graph-based anomaly mining. I aim to present a broad view of each area, and discuss classes of main research problems, recent trends and future directions. I conclude with key take-aways and overarching open problems. Disclaimer. I try to provide an overview of past and recent trends in both areas within 4 pages. Undoubtedly, these are my personal view of the trends, which can be organized differently. For brevity, I omit all technical details and refer to corresponding papers. Again, due to space limit, it is not possible to include all (even most relevant) references, but a few representative examples.