We discuss differential geometric properties of holomorphic cone structures that arise from algebraic geometry. Holomorphic cone structures are natural objects with lots of examples, but not very widely known. So we start with reviewing the relevant concepts in differential geometry in the first section. In the second section, we explain a key classification result in differential geometry from [9]. In the third section, we recall how rational curves in algebraic geometry give rise to natural cone structures. In the fourth section, we report on the joint work [6] with Qifeng Li.