Since the discovery of the inner nuclear transmembrane protein emerin in the early 1990s, nuclear envelope (NE) components and related involvement in nuclei integrity and functionality have been highly investigated. The NE is composed of two distinct lipid bilayers described as the inner (INM) and outer (ONM) nuclear membrane. NE proteins can be specifically “integrated” in the INM (such as emerin and SUN proteins) or in the ONM such as nesprins. Additionally, flanked to the INM, the nuclear lamina, a proteinaceous meshwork mainly composed of lamins A and C completes NE composition. This network of proteins physically interplays to guarantee NE integrity and most importantly, shape the bridge between cytoplasmic cytoskeletons networks (such as microtubules and actin) and the genome, through the anchorage to the heterochromatin. The essential network driving the connection of nucleoskeleton with cytoskeleton takes place in the perinuclear space (the space between ONM and INM) with the contribution of the LINC complex (for Linker of Nucleoskeleton to Cytoskeleton), hosting KASH and SUN proteins interactions. This close interplay between compartments has been related to diverse functions from nuclear integrity, activity and positioning through mechanotransduction pathways. At the same time, mutations in NE components genes coding for proteins such as lamins or nesprins, had been associated with a wide range of congenital diseases including cardiac and muscular diseases. Although most of these NE associated proteins are ubiquitously expressed, a large number of tissue-specific disorders have been associated with diverse pathogenic mutations. Thus, diagnosis and molecular explanation of this group of diseases, commonly called “nuclear envelopathies,” is currently challenging. This review aims, first, to give a better understanding of diverse functions of the LINC complex components, from the point of view of lamins and nesprins. Second, to summarize human congenital diseases with a special focus on muscle and heart abnormalities, caused by mutations in genes coding for these two types of NE associated proteins.