Due to the recent breakthroughs of deep generative models, the fake faces, also known as deepfake which has been abused to deceive the general public, can be easily produced at scale and in very high fidelity. Many works focus on exploring various network architectures or various artifacts produced by deep generative models. Instead, in this work, we focus on the loss functions which have been shown to play a significant role in the context of face recognition. We perform a thorough study of several recent state-of-the-art losses commonly used in face recognition task for deepfake classification and detection since the current deepfake is highly related to face generation. With extensive experiments on the challenging FaceForensic++ and Celeb-DF datasets, the evaluation results provide a clear overview of the performance comparisons of different loss functions and generalization capability across different deepfake data.