In most of liquids, densities increase as temperature decreases. However, the densities of water and water-like liquids, such as silicon and germanium, are anomalous, which increase as temperature increases. Such substances also show other anomalous behaviors, such as diffusivity anomalies (diffusivities increase as density increases), and thermodynamic anomalies (the fluctuations increase as temperature decreases). The chemical properties of these materials are very different from each other, but they all share similar physical properties. Further studies indicate that most of them have two distinct liquid states, i.e., a low-density liquid and a high-density liquid, and a first order liquid-liquid phase transition (LLPT) between these two liquids. We mainly discuss the anomalous properties of materials each of which has a predicted LLPT and their relations with anomalous behaviors (thermodynamic, dynamic and structural) as those of water and water-like liquids, such as hydrogen and gallium. In particular, we discuss the supercritical phenomenon of the liquid-liquid phase transition of hydrogen, as well as the liquid-liquid phase transition of gallium and its relation with the thermodynamic, dynamic, and structural anomalies. It is found that the liquid hydrogen and gallium both have the LLPT and share similar anomalous behaviors as water and water-like liquids, such as density anomaly, dynamics anomaly, thermodynamic anomaly Since the chemical properties of these materials are very different from those of others having the LLPT, the anomalous behaviors may be common features for substances predicted to have the LLPT.