Young and rotation-powered neutron stars (NSs) are commonly observed as rapidly-spinning pulsars. They dissipate their rotational energy by emitting pulsar wind with electromagnetic radiation and spin down at a steady rate, according to the simple steadily-rotating magnetic dipole model. In reality, however, multiwavelength observations of radiation from the NS surface and magnetosphere have revealed that the evolution and properties of NSs are highly diverse, often dubbed as 'NS zoo'. In particular, many of young and highly magnetized NSs show a high degree of activities, such as sporadic electromagnetic outbursts and irregular changes in pulse arrival times. Importantly, their magnetic field, which are the strongest in the universe, makes them ideal laboratories for fundamental physics. A class of highly-magnetized isolated NSs is empirically divided into several subclasses. In a broad classification, they are, in the order of the magnetic field strength (B) from the highest, 'magnetars' (historically recognized as soft gamma-ray repeaters and/or anomalous x-ray pulsars), 'high-B pulsars', and (nearby) x-ray isolated NSs. This article presents an introductory review for non-astrophysicists about the observational properties of highly-magnetized NSs, and their implications. The observed dynamic nature of NSs must be interpreted in conjunction with transient magnetic activities triggered during magnetic-energy dissipation process. In particular, we focus on how the five fundamental quantities of NSs, i.e. mass, radius, spin period, surface temperature, and magnetic fields, as observed with modern instruments, change with evolution of, and vary depending on the class of, the NSs. They are the foundation for a future unified theory of NSs.