Fluid injection is a common practice in the Oil and Gas industry found in many applications such as waterflooding and disposal of produced fluids. Maintaining high injection rates is crucial to guarantee the economic success of these projects; however, there are geomechanical risks and difficulties involved in this process that may threat the viability of fluid injection projects. Near wellbore reduction of permeability due to pore plugging, formation failure, out of zone injection, sand production, and local compaction are challenging the effectiveness of the injection process. Due to these complications, modeling and simulation has been used as an effective tool to assess injectors' performance, however, different problems have yet be addressed. In this paper, we review some of these challenges and the solutions that have been proposed as a primary step to understand mechanisms affecting well performance.