Several definitions of the crystal electric field (CEF) have been used over time and their variety has lead to many misunderstandings, in both theoretical and experimental literature. Two categories of definitions can be mentioned, the first being the operators equivalents introduced by Stevens in 1952 and the second being the crystal-field operators, introduced later by Wybourne and expanded on the Racah spherical tensors. This paper aims at providing some clarification in this field. We first make a review of several expressions introduced in various references to compute crystal-field operators and we make connections between them. Then, we introduce an explicit way to compute crystal-field operators, in terms of j and m as well as in terms of J^2 and Jz. We eventually give some connections between the Stevens operators equivalents and the crystal-field operators.