Hardware impairments (HWIs) impose a huge challenge on modern wireless commu- nication systems owing to the characteristics like compactness, least complexity, cost ef- fectiveness and high energy efficiency. Numerous techniques are implemented to minimize the detrimental effects of these HWIs ,however, the residual HWIs may still appear as an additive distortion, multiplicative interference, or an aggregate of both. Numerous studies have commenced efforts to model one or the other forms of hardware impairments in the ra- dio frequency (RF) transceivers. Many presented the widely linear model for in-phase and quadrature imbalance (IQI) but failed to recognize the impropriety induced in the system because of the self-interfering signals. Therefore, we have presented not only a rigorous ag- gregate impairment model along with its complete impropriety statistical characterization but also the appropriate performance analysis to quantify their degradation effects. Lat- est advances have endorsed the superiority of incorporating more generalized impropriety phenomenon as opposed to conventional propriety. In this backdrop, we propose the improper Gaussian signaling (IGS) to mitigate the drastic impact of HWIs and improve the system performance in terms of achievable rate and outage probability. Recent contributions have advocated the employment of IGS over traditional proper Gaussian signaling (PGS) in various interference limited scenarios even in the absence of any improper noise/interference. It is pertaining to the additional degree of freedom (DoF) offered by IGS, which can be optimized to reap maximum benefits. This reduced-entropy signaling is the preferred choice to pose minimal interference to a legitimate network yielding another mechanism to tackle undesired interference. Evidently, the incorporation of both inherent and induced impropriety characteristics is critical for effective utilization. Most of the recent research revolves around the theoretical analysis and advantages of improper signaling with minimal focus on its practical realization. We bridge this gap by adopting and optimizing asymmetric signaling (AS) which is the finite discrete implemen- tation of the improper signaling. We propose the design of both structural and stochastic shaping to realize AS. Structural shaping involves geometric shaping (GS) of the symbol constellation using some rotation and translation matrices. Whereas, stochastic shaping as- signs non-uniform prior probabilities to the symbols. Furthermore, hybrid shaping (HS) is also proposed to reap the gains of both geometric and probabilistic shaping. AS is proven superior to the conventional M-ary symmetric signaling in all of its forms. To this end, probabilistic shaping (PS) demonstrates the best trade-off between the performance en- hancement and added complexity. This research motivates further investigation for the utilization of impropriety concepts in the upcoming generations of wireless communications. It opens new paradigms in inter- ference management and another dimension in the signal space. Besides communications, the impropriety characterization has also revealed numerous applications in the fields of medicine, acoustics, geology, oceanography, economics, bioinformatics, forensics, image processing, computer vision, and power grids.