The study of two-dimensional materials is a relatively new field of interest, which became rapidly popular with the discovery of graphene in 2004. Soon thereafter, a large number of other two-dimensional materials have been discovered, such as transition metal dichalcogenides. The properties of such materials are significantly different, as well as typically more interesting compared to their respective three-dimensional allotropes. Owing to such properties, these materials hold a good potential to be utilized in the field of electronics and similar areas. To enable the use and manufacturing of devices made of two-dimensional materials, it is necessary to improve their synthesis methods, as well as increase the control of defects and quality of materials during synthesis. In this work, we particularly focus on the two of the most commonly studied materials: graphene and MoS2, and we show their main properties and applications. We present the syntheses through the method of chemical vapor deposition, which shows a great potential for the quality growth of two-dimensional materials. Here, the graphene was grown on the copper foil, while the MoS2 was grown on the SiO2/Si substrate. To obtain a better growth model, it is necessary to utilize adequate methods for the analysis and assessment of quality of synthesized samples. Optical microscopy has proven to be an efficient and powerful initial tool for data collection. However, we need to develop statistical methods to process the collected data with the aim of further extracting useful information about the synthesized samples. In this work, we present and develop two methods for the analysis of images obtained from the optical microscope, both adapted from the field of deep and machine learning. The first method belongs to the class of deep unsupervised autoencoders. Using this approach, we obtain the information about the shape of the single grain graphenes by analysing the images obtained from the optical microscope directly. The second method is, likewise, a deep neural network, but based on the UNet architecture. This neural network has been successfully trained to detect and segment the areas of MoS2 from the substrate on the collected images with high accuracy. We show that with this method, the computer can efficiently track the changes of important parameters in time, such as the size of single grains and their circumference. All samples used throughout this work have been synthesized at the Institute of Physics in Zagreb. MoS2 has been recorded with the optical microscope during its growth, while the samples of graphene have been collected after the synthesis completion.