The hard disk drive technology is well-established now as a multi-billion dollar industry. Ever since the advent of hard disk magnetic recording media for computers in the 1950's, their data storage density has been increasing at an exponential rate in response to the growing need for memory storage space. Data in bits of 0 and 1 is written in the magnetic layer (ML) of perpendicular magnetic recording (PMR) media in blocks of effectively uniform magnetizations in hexagonal closed-packed (HCP) structure Co-rich magnetic grains (separated by a nonmagnetic intergranular phase) in directions perpendicular to the disk surface. While the densely packed grains are randomly positioned across the ML as fabricated, the magnetization blocks are written in precisely addressed locations along tracks using the write pole of the read/write head of the memory device. The magnetic nanocrystals form the medium for the writing of information. Obtaining a desirable nanostructure in the ML is of critical importance to the performance of the device. In order to reduce the physical bit size, the ML grain size has been trimmed down over time to maintain a desired signal-to-noise ratio. This progress has been supported by research focused on characterizing the grain structure in terms of size and size distribution. The ML nanostructure must be studied at the nanoscale to facilitate further reduction of the bit size. The transmission electron microscope (TEM) is the ideal tool for examining the nanoscale features of the PMR media. In this work, the TEM was utilized to develop techniques for the study, at the atomic scale, of key structural features of the PMR media which had not been experimentally examined before. The structural and crystallographic correlations between the grains of the ML and its RU seed layer were identified experimentally by observing the two layer structures simultaneously using the energy dispersive spectrometry technique -- a method of studying the chemical constituents of each layer with a scanning TEM technique. This study revealed the one-to-one grain structure relationship. The crystallographic relationship between the nanocrystals in the two layers was identified by analysing the observed Moiré fringes in TEM images. In addition, clusters of grains with common crystallographic orientations in the ML were identified using a novel 2 1/2 dimensional dark field imaging technique previously used to study crystal orientations in physical polycrystalline material systems. Furthermore, through the use of a spherical-aberration-corrected TEM, key structural features of the ML with potential consequences in the performance of the device were revealed at the atomic scale. This revelation was achieved by eliminating the delocalization effect resulting from the objective lens spherical aberration by which, in conventional TEM images, the lattice fringes are extended beyond the crystal boundaries. The newly observed features include the nanocrystalline bridges connecting neighboring magnetic grains through the amorphous intergranular phase and faceting of the grains along their prominent plane systems. Thus, the TEM is shown to be a powerful tool to study different structure-property relationships in these important materials. The results presented in this work are expected to contribute to the on-going efforts to increase the volume of information accommodated in more compact devices after the fine-scale structures observed using advanced microscopy are correlated with the magnetic properties of the device.