Anderson localization, originally proposed by the physicist Philip W. Anderson in 1958, describes the confinement of waves in disordered systems. Expanding upon this concept, Many-Body Localization (MBL) explores the localization of interacting particles in disordered environments. Recent research has also revealed the possibility of Stark MBL, where the localization occurs in the absence of disorder under the influence of external fields. Experimental investigations have played a pivotal role in elucidating the Anderson localization to disorder-driven MBL and further to Stark MBL. These experiments provide valuable information on the unique properties and experimental signatures of the MBL transition. In this thesis, we undertake a comprehensive investigation of the MBL transition in spinless fermion chains using different models. Our examination encompasses multiple aspects, including the analysis of key indicators such as Entanglement Entropy, Level Statistics, and Inverse Participation Ratio. Furthermore, we study the time dynamics, with a specific focus on the long-time evolution regime. Within the MBL phase, we expect the dynamics of the system to freeze, which inhibits it from reaching thermal equilibrium. By analyzing the time evolution of the spinless fermion chains within the MBL phase, our goal is to understand the persistent non-thermal behavior and the absence of equilibrium. Lastly, we compare the differences between disorder-driven MBL and Stark MBL, shedding light on their distinct characteristics and underlying mechanisms. Understanding the contrasting features of these two types of localization phenomena contributes to our overall understanding of Stark MBL. Through our comprehensive exploration, we aim to contribute to the knowledge of the MBL transition. By investigating the behavior of spinless fermion chains under different conditions, we provide crucial insights into the MBL transition, furthering our understanding of this fascinating phenomenon and its broader implications for condensed matter physics and quantum many-body systems in non-equilibrium physics.