This paper deals with modern production management methodologies: Lean management and Industry 4.0, as well as a real-life example from production with the application of selected methods. The introductory part of the paper contains the history, that is, the development of Lean management and Industry 4.0, as well as the basic principles and waste defined by Lean. Lean management is a philosophy of process management (production, but also other) and includes a wide range of methodologies that have been developed over many years. This work covers the well-known and most frequently used methods such as SMED, 5S, VSM, Kaizen, and TPM. Each Lean tool serves a different purpose and can be used in different situations. So 5S is most often used to organize the workplace so that all tools are easily accessible. SMED is applied to speed up tool changes while production is at a standstill. VSM graphically displays the process with all its items and sub-processes, which makes it easier to spot losses. The Kaizen approach organizes a systematic way of solving problems in teams. In the second part of the work, the technologies belonging to the last industrial revolution called Industry 4.0 are discussed. Industry 4.0 is a collective name for the most modern technologies that are developed and implemented in the industry (and elsewhere). There are many such technologies and they are continuously being improved. The paper deals with the most common and well-known technologies such as the Internet of Things, additive manufacturing, and altered reality. The Internet of Things primarily connects machines and enables their mutual communication. Additive manufacturing is also called 3D printing and is used in industry for rapid prototyping. Altered reality allows the display of desired elements in real-time added to reality through special glasses or in other ways. In the last part of the paper, one production company and the processes that take place within it will be described. A process has been selected in the company where selected methods of Lean management and technologies that belong to the beginnings of the process of transforming the company into Industry 4.0 will be presented.