It is becoming increasingly easy to automatically replace a face of one person in a video with the face of another person by using a pre-trained generative adversarial network (GAN). Recent public scandals, e.g., the faces of celebrities being swapped onto pornographic videos, call for automated ways to detect these Deepfake videos. To help developing such methods, in this paper, we present the first publicly available set of Deepfake videos generated from videos of VidTIMIT database. We used open source software based on GANs to create the Deepfakes, and we emphasize that training and blending parameters can significantly impact the quality of the resulted videos. To demonstrate this impact, we generated videos with low and high visual quality (320 videos each) using differently tuned parameter sets. We showed that the state of the art face recognition systems based on VGG and Facenet neural networks are vulnerable to Deepfake videos, with 85.62% and 95.00% false acceptance rates (on high quality versions) respectively, which means methods for detecting Deepfake videos are necessary. By considering several baseline approaches, we found the best performing method based on visual quality metrics, which is often used in presentation attack detection domain, to lead to 8.97% equal error rate on high quality Deepfakes. Our experiments demonstrate that GAN-generated Deepfake videos are challenging for both face recognition systems and existing detection methods, and the further development of face swapping technology will make it even more so.