X-ray surveys are an effective way to study growing supermassive black holes (SMBHs) in galaxy centers, as actively accreting SMBHs manifest themselves as active galactic nuclei (AGN) that can be observed in the X-ray in most cases. Through studying AGNs in X-ray survey fields that have extensive multiwavelength data coverage, we can probe how SMBH growth links with their host galaxies over cosmic history. Previously, researchers mainly linked SMBH growth with stellar mass (M⋆) or star formation rate (SFR). In this dissertation, we utilize morphological information to show that among star-forming (SF) galaxies, long-term average SMBH accretion rate (BHAR) relates to host-galaxy compactness (Chapter 2). We found that the relation between BHAR and host-galaxy compactness is more fundamental than the relation between BHAR and M⋆ or SFR (Chapter 3). This dissertation also provides key results from the XMM-Spitzer Extragalactic Representative Volume Survey (XMM-SERVS), which will benefit studies of SMBH growth in the next decade with a large sample of AGNs that have superb multiwavelength data. The detection of X-ray point sources in two of the XMM-SERVS survey fields is presented in Chapter 4. In Chapter 5, multiwavelength counterpart identification, photometric-redshift calculation, and source classification for X-ray sources in the XMM-SERVS survey fields are presented; most of the X-ray point-like sources detected are classified as AGNs, showing SMBH growth over the full range of cosmic environments. A Hyper Suprime-Cam (HSC) forced-photometry catalog that provides optical coverage for one of the XMM-SERVS survey fields is presented in Chapter 6. Apart from these works that focus on "Active Galactic Nuclei Studies in Cosmic X-ray Survey Fields", this dissertation also includes my other two first-author works in the appendices, where X-ray observational studies of weak-line quasars (WLQs) are presented. By studying these quasars with exceptional spectroscopic properties, we found good supporting evidence for optically thick inner accretion disks among quasars with high Eddington ratios.