Nowadays, complex and expensive neural architectures are seen by many as a way to improve the performance of existing models in image recognition, voice recognition, translation, and other tasks. Such a perspective caused an increased interest in expert architecture engineering within Deep Learning. Fueled by this interest, neural architecture search originated as a promising way to automate the tedious process of constructing a deep neural network by hand. Over the last five years, we have seen an increasing number of works focusing all efforts on studying the impact of automating deep neural network design. The spotlight has recently turned from automatically discovering classification models to other more complex tasks. Motivated by a desire for high-resolution images in real-world user-centered and expert computer vision applications, architecture search for super-resolution image restoration centers in approaches capable of automatically finding efficient and well-performing models. Here, we present a survey that, beyond delving into an overview of modern approaches to automatic neural network design, focuses on the recollection and study of neural architecture search approaches that have directed their efforts at the super-resolution image restoration tasks and future lines of research found within this emerging area of study.