The energy consumption in residential buildings is mainly combined with the interior environment's heating and cooling energy demand. One solution is to reduce these energy consumptions by implementing a phase change material (PCM) based thermal energy storage (TES) technique. Thermal energy storage with phase change materials can be applied for peak electricity demand saving or increased energy efficiency in heating, ventilation, and air-conditioning (HVAC) systems. The primary grid benefit of thermal energy storage is load shifting and shedding by replacing heating, ventilation, and air conditioning system operation during peak times and recharging the storage system during off-peak times. Additional efficiency benefits come from shifting HVAC system operations to periods when the system can operate more efficiently and at a lower cost. This paper discusses the present state-of-the-art PCMs for thermal energy storage systems for buildings space heating/cooling applications and the limitations of incorporating phase change materials that negatively impact the performance. The limits are supercooling, low thermal conductivity, phase segregation, fire safety, corrosion, and cost. This study briefly explored how some of these issues can be limited or eliminated. The application of phase change materials has been demonstrated as a solution to decrease the energy demand of an apartment building. Results for two available and environmentally friendly PCMs (BioPCM and DuPont Energain) with different melting ranges applied inside the exterior walls and the roof is analyzed and presented. Simulations have been performed with and without the application of PCM materials. It was demonstrated that PCM could store heat energy from solar radiation and the surrounding environment, thus reducing energy consumption for heating and cooling scenarios.