In this paper we survey and analyze modern neural-network-based facial landmark detection algorithms. We focus on approaches that have led to a significant increase in quality over the past few years on datasets with large pose and emotion variability, high levels of face occlusions - all of which are typical in real-world scenarios. We summarize the improvements into categories, provide quality comparison on difficult and modern in-the-wild datasets: 300-W, AFLW, WFLW, COFW. Additionally, we compare algorithm speed on CPU, GPU and Mobile devices. For completeness, we also briefly touch on established methods with open implementations available. Besides, we cover applications and vulnerabilities of the landmark detection algorithms. Based on which, we raise problems that as we hope will lead to further algorithm improvements.