Machine learning (ML) is rapidly gaining its popularity in the field of materials science due to its exceptional ability to learn from data to guide experimentalists, thus reducing traditional trial and error loops coupled with human intuition; as well as to replace time consuming ab initio calculations. Of course, the foundation of ML is data (preferably large and of good quality). Currently, there are well organised and maintained experimental (ICSD, CSD, HTEM, etc.) and theoretical (MP, AFLOW, OQMD, etc.) databases that power ML models, but it is not uncommon that researchers collect their own databases by High-throughput Density Functional Theory calculations, High-throughput Experiments or screening the literature.
I have highlighted several cases below where ML is applied in materials research. However, this is not an exhaustive list, meaning there is many more applications, and growing.
- Structure-property prediction regression models 
- Classification models to screen-down a large database to find candidate materials for a desired material class 
- Classification/regression models for material characterisation (e.g. analyse space group using XRD data )
- Natural language processing (NLP) models for automatic data extraction from literature [chemdataextractor], capture materials knowledge by automatically reading Millions of papers , future research trend prediction etc.
- Active learning and Bayesian optimisation to guide experiments 
- Material/molecule generation using reinforcement learning 
- Dimensionality reduction for data visualization 
I strongly recommend NPJ Computational Materials, which is a well received, specialised journal in this field. Following are two good review papers I came across.
You would also want to check out the tools below for high-throughput DFT calculations and analyses that are usually coupled with ML studies in computational materials science.
- pymatgen - open-source python library for materials analysis
- fireworks - open-source python package for managing
- atomate - python package built on top of pymatgen & fireworks
to execute workflows. It can be integrated with VASP which makes it
easier to run a series of VASP calculations using a few lines of
- AFLOW ML - ML tool provided by AFLOW repository
Finally, the true potential of Artificial Intelligence (AI) is yet to be explored in the field of materials science; and by the look of it, there is lot more opportunities. Some of you might have heard of Generative Adversarial Networks (GANs) that were recently used to generate realistic images of people that do not exist in the world! Check out StyleGAN by NVIDIA. Who knows if these GANs or other generative AI models will be used to generate new synthesizable compounds!