This paper is devoted to drum and vibrating screens and addresses their possible application in the process of screening municipal and mineral waste. The basis for this article are conclusions from a relevant research that has been conducted for many years at the Department of Process Equipment of the Lodz University of Technology. The authors describe the principles of operation and significant parameters of the presented screening machines. They describe the deposit movement in the screen drum, specify critical velocity and rotational speed for the drum dimensions between 0.5 and 3.0 m and discuss the power and capacity of the presented machinery. The paper involves basic types of drum screens, however, new designs of the equipment are proposed. Those new designs include machines equipped with cone and cascade sieves. The advantage of such solutions is that particulate material can be screened along the sieve with a zero inclination of the sieve axis. Furthermore, drums can take the form of prisms with regular polygonal bases. Drums designs enable the use of equipment facilitating the screening process. Examples of such solutions include a movable cross used for cleaning sieve holes and, in the case of very fine particulate materials, the use of blow-in inside the screen drum. Drum screens provide for both dry and wet operation. Screening efficiency in industrial drum screens for rock is 40–60%. Another group of equipment that should be used in processing mineral waste are screens with flat sieves. They have been used for many years in the processing of minerals and the multitude of their designs provides for new opportunities for other branches of industry. A single-plane screen is a good solution for screening waste. The sieve of this screen performs a plane motion of any trajectory shape. Another type of equipment that can be used for segregating waste is an elliptical bi-axial screen. This machine enables the shaping of the screen motions trajectory in a vibrating motion. Both screens may be horizontal, as the arrangement of the power transmission system provides for the movement of the material layer on a horizontal sieve. Bi-axial vibrational screens driven with rotating (bi-axial) vibrators in various designs are currently the most common ones. An example of a modern screening machine is a membrane screen in which only the sieve, and not the entire riddle, moves. Special methods and equipment are used for the screening of fine and very fine particulate materials that are supposed to intensify the screening process. One of the examples is the use of additional sieves in a multi-deck screen. The sieves are selected according to the characteristic dimensions of sieve holes, on the basis of the feed particulate composition. Another example of the intensification of screening is the use of gradual screening (involving the use of additional sieves). There is also the sieve holes enlargement method. It involves the use of sieve holes larger than the assumed limit of classification. This method proves that sometimes it is advisable to slightly compromise the screening efficiency in order to increase capacity. All the types of screens presented in the paper may be successfully used for screening mineral and municipal waste. Furthermore, screens with flat sieves enable the construction of different process lines and they could be easily adapted to the changing waste segregation process requirements.