In recent years, extensive research in the field of Deep Learning (DL) has led to the development of a wide array of machine learning algorithms dedicated to solving complex tasks such as image classification or speech recognition. Due to their unprecedented ability to explore large volumes of data and extract meaningful hidden structures, DL models have naturally drawn attention from various fields in science. Analytical chemistry, in particular, has successfully benefited from the application of DL tools for extracting qualitative and quantitative information from high-dimensional and complex chemical measurements. This report provides introductory reading for understanding DL machinery and reviews recent analytical applications of these powerful algorithms.