High requirements imposed by the competitive industrial environment determine the development directions of applied manufacturing methods. 3D printing technology, also known as additive manufacturing (AM), currently being one of the most dynamically developing production methods, is increasingly used in many different areas of industry. Nowadays, apart from the possibility of making prototypes of future products, AM is also used to produce fully functional machine parts, which is known as Rapid Manufacturing and also Rapid Tooling. Rapid Manufacturing refers to the ability of the software automation to rapidly accelerate the manufacturing process, while Rapid Tooling means that a tool is involved in order to accelerate the process. Abrasive processes are widely used in many industries, especially for machining hard and brittle materials such as advanced ceramics. This paper presents a review on advances and trends in contemporary abrasive machining related to the application of innovative 3D printed abrasive tools. Examples of abrasive tools made with the use of currently leading AM methods and their impact on the obtained machining results were indicated. The analyzed research works indicate the great potential and usefulness of the new constructions of the abrasive tools made by incremental technologies. Furthermore, the potential and limitations of currently used 3D printed abrasive tools, as well as the directions of their further development are indicated.