In neuromorphic computing, different learning mechanisms are being widely adopted to improve the performance of a specific application. Among these techniques, Spike-Timing-Dependent Plasticity (STDP) stands out as one of the most favored. STDP is simply managed by the temporal information of an event, which is biologically inspired. However, most of the prior works on STDP are focused on circuit implementation or software simulation for performance evaluation. Previous works also lack a comparative analysis of the performances of different STDP implementations. This study aims to provide a comprehensive assessment of STDP, centering on the performance across various applications such as classification (static and temporal datasets), control, and reservoir computing. Different applications necessitate distinct STDP configurations to achieve optimal performance with the neuroprocessor. Additionally, this work introduces an Application-Specific Integrated Circuit (ASIC) design of STDP circuitry. The design is based on current-controlled memristive synapse principles and utilizes 65nm CMOS technology from IBM. The detailed presentation includes circuitry specifics, layout, and performance parameters such as energy consumption and design area.