Support Vector Machines (SVMs) have proven to yield high accuracy and have been used widespread in recent years. However, the standard versions of the SVM algorithm are very time-consuming and computationally intensive; which places a challenge on engineers to explore other hardware architectures than CPU, capable of performing real-time training and classifications while maintaining low power consumption in embedded systems. This paper proposes an overview of works based on the two most popular parallel processing devices: GPU and FPGA, with a focus on multiclass training process. Since different techniques have been evaluated using different experimentation platforms and methodologies, we only focus on the improvements realized in each study.