The concept of centrality and centrality measures are well-known and frequently used in social network analysis. They are also implemented in numerous software packages. However, that does not mean that it is easy to apply them correctly. This paper aims to introduce the most frequently used centrality measures, but more importantly to point out the problems related to their application and to sketch potential solutions for these problems. First, three basic centrality measures are introduced: degree, betweenness, and closeness. There are three broad categories of issues with centrality measures. These categories are: inadequate operationalisation of centrality measures, explanation of their distribution, and interdependence of observation in statistical modelling. A typology of flows in the network is presented as a potential solution allowing for transparent operationalisation. The so-called positional approach is another potential solution allowing for conceptually and computationally rigorous definition of centrality measures. Lastly, statistical models for network data are introduced as a way to deal with interdependence of observations. In the conclusion, challenges for measuring centrality in bipartite and multiplex networks are discussed.