Domain adaptation of GANs is a problem of fine-tuning the state-of-the-art GAN models (e.g. StyleGAN) pretrained on a large dataset to a specific domain with few samples (e.g. painting faces, sketches, etc.). While there are a great number of methods that tackle this problem in different ways there are still many important questions that remain unanswered. In this paper, we provide a systematic and in-depth analysis of the domain adaptation problem of GANs, focusing on the StyleGAN model. First, we perform a detailed exploration of the most important parts of StyleGAN that are responsible for adapting the generator to a new domain depending on the similarity between the source and target domains. In particular, we show that affine layers of StyleGAN can be sufficient for fine-tuning to similar domains. Second, inspired by these findings, we investigate StyleSpace to utilize it for domain adaptation. We show that there exist directions in the StyleSpace that can adapt StyleGAN to new domains. Further, we examine these directions and discover their many surprising properties. Finally, we leverage our analysis and findings to deliver practical improvements and applications in such standard tasks as image-to-image translation and cross-domain morphing.