The Trotter product formula is a basic tool for approximating dynamics generated by sums of operators. For bounded operators, quantitative error bounds are well understood and are typically expressed as operator-norm estimates in terms of commutators. For unbounded generators, convergence of the Trotter product is not automatic, and even when it holds, operator-norm convergence may fail. Convergence rates must then often be expressed in terms of properties of the initial state, such as its regularity or energy. In this talk I will give an overview of several approaches to Trotter convergence rates for unbounded generators. These include state-dependent error estimates, bounds obtained from the geometry of Lie group representations, convergence rates based on interpolation methods, and energy-constrained estimates for dynamics that control the growth of a reference energy. I will emphasise the common ideas behind these approaches, the different assumptions under which they apply, and some examples.