Play has been present in a child's life since birth. It is one of the most important activities of a child and through it the child develops, has fun, adopts and learns about the world around him. By playing it improves and influences it's physical, cognitive, emotional and social development. Considering that play has been present in a child's life since their earliest age and is therefore close them, it would be unimaginable that the game disappears by going to school. Therefore, it is important to include play in the primary education in a correct and purposeful way and make it close to the child. As already mentioned the need for play is merged by the need of movement and it is the school classes of Physical Education that enable the fulfillment of the above. Through the application of elementary and relay games, physical education is achieved and their goal is to develop and maintain motor and functional abilities and to improve the learned motor skills. It is also possible to notice the educational aspect of the game thanks to which it is indicated through play and then influenced on changes in the child's behaviour. Not only does the child adopt rules of behaviour by playing but the child also adopts the rules of the game and nurtures cooperation with others. Cooperation and community development is especially emphasized in relay games. It is the teacher who will know how to choose the appropriate games in order to achieve the above. However, in order for the teacher to be able to choose appropriate games, it is important to know the psychophysical characteristics of the child and to choose games accordingly. In order to encourage and point out the importance of including a variety of games in the teaching process, this paper seeks to raise awareness of children's need for play as well as its positive effects on all aspects of development. Therefore, examples of contact and non-contact elementary games with a corresponding descriptions are given, as well as examples of relay games listed and described according to the variants of their implementation.