The discussion about counting methods in bibliometrics is often reduced to the choice between full and fractional counting. However, several studies document that this distinction is too simple. The aim of the present study is to give an overview of counting methods in the bibliometric literature and to provide insight into their properties and use. A mix of methods is used. In the preliminary results, a literature review covering 1970-2018 identified 29 original counting methods. Seventeen were introduced in the period 2010-2018. Twenty-one of the 29 counting methods are rank-dependent and fractionalized meaning that the authors of a publications share 1 credit but do not receive equal shares, for example harmonic counting. The internal and external validation of the counting methods are assessed. Three criteria for well-constructed bibliometric indicators - adequacy, sensitivity, and homogeneity - are used to assess the internal validity. Regarding the external validation of the counting methods, it is investigated whether the intentions in the studies that introduced the 29 counting methods comply with the subsequent use of the counting methods. This study has the potential to give a solid foundation for the use of and discussion about counting methods.