Summary: Let \(\mathbb{K}\) be an algebraically closed field of characteristic \(p > 0\) and let \(G\) be a connected reductive algebraic group over \(\mathbb{K}\). Under some standard hypothesis on \(G\), we give a direct approach to the finite \(W\)-algebra \(U(\mathfrak{g},e)\) associated to a nilpotent element \(e \in \mathfrak{g} = \mathrm{Lie}\, G\). We prove a PBW theorem and deduce a number of consequences, then move on to define and study the \(p\)-centre of \(U(\mathfrak{g},e)\), which allows us to define reduced finite \(W\)-algebras \(U_{\eta}(\mathfrak{g},e)\) and we verify that they coincide with those previously appearing in the work of A. Premet [Mosc. Math. J. 7, No. 4, 743–762 (2007; Zbl 1139.17005); Adv. Math. 225, No. 1, 269–306 (2010; Zbl 1241.17015)]. Finally, we prove a modular version of Skryabin’s equivalence of categories, generalizing recent work of the second author [Math. Z. 285, No. 3–4, 685–705 (2017; Zbl 1405.17039)].