The perplexing and intriguing world of biological systems has inaugurated a new research field in statistical physics: out-of-equilibrium systems, known as active matter that mimic systems in the biological world around us from a statistical mechanical point of view. These systems exhibit captivating collective dynamics such as selfsustained pattern formation. Self-organization of motors and microtubules within the cell, swarming colonies of bacteria, and starling murmuration are some fascinating patterns in nature that organize themselves independently, without external control. Numerous computational, theoretical, and experimental models have been developed to unravel the physics of active matter system.In this thesis, we employ several agent-based minimal models to study self-propelled particles to explore the key parameters that play a significant role in their dynamics and self-organization.We develop a hexagonal lattice model to study the dynamics of passive "tracers" in the presence of active crowders where the tracer is pushed by the active particles, which leads to enhanced diffusion. We show that the degree to which this diffusion is enhanced depends crucially on the activity and the density of the crowders. Furthermore, we show that a decrease in the diffusion coefficient of passive particles is an explicit consequence of the local accumulation of active crowders in the system.