In recent years there has been rapid progress in the research of Active Galactic Nuclei (AGNs), such as central super-massive black holes (SBH), accretion processes, and their host galaxies. Using data from ROSAT point sources, we found that the soft X-ray spectra of narrow-line Seyfert 1 galaxies (NLS1s) and Blazars become harder during X-ray flux increases, while the spectra of broad-line AGNs (BL AGNs) become softer. From ASCA data, we found that NLS1s and BL AGNs follow the same $\sigma^{2}-M_{MBH}$ relation, where $\sigma^{2}$ is the excess variance in the hard X-ray band. With the accretion efficiency of AGNs, we found that most of the radio-loud quasars possibly possess a Kerr SBH, while the Seyfert 1 galaxies and radio-quiet quasars possess Schwarzschild SBH. We also studied the relation between the central black holes and their host galaxies. It was found that NLS1s appear to have genuinely lower MBH/bulge mass ratios. And the width of the [O III] line is not a good tracer of host velocity dispersion. NLS1s play a special role in our understanding of the evolution of galaxies and their central SBHs.