The main motivations for the development of research in the area of appropriate additives for asphalt and bitumen are the enhancement of their properties and improvement of their production process, including the reduction in environmental burden. Many additives improve the properties of mineral–asphalt mixtures. Traditionally, additives such as the following are applied: elastomers, plastomers, latexes, rubber powder, resins, and others. Currently, the modification of asphalt and bitumen materials by traditional additives can be replaced by nanomaterials that better fit the requirements of modern industry. New solutions are required, which has led to years of studies researching micro- and nano-additives. The main aim of the article is to analyze contemporary research where micro- and nano-additives were applied to asphalt and bitumen and summarize the advantages and disadvantages of the implementation of these additives for road construction. The article studied the state of the art in this area based on the literature research. It presents the possible materials’ solutions, including their properties, used technology, and featured trends for road construction. The challenges for further projects are discussed, especially environmental issues.