The finite cell method is a combination of a fictitious domain method with a finite element method. It is based on the replacement of the possibly complicated physical domain by an embedding domain of a geometrically simple shape which can easily be meshed. The variational formulation of the problem and its finite element discretization is defined on the embedding domain. An indicator function is used to incorporate the geometry of the physical domain. Mainly two computational error sources occur in the finite cell method: the discretization error and the quadrature error. The talk presents concepts of a posteriori error control for the finite cell method. The focus is on a residual-based error control for the reliable estimation of the discretization error with respect to the energy norm and on the application of the dual weighted residual approach (DWR), which enables the control of the error in terms of a user-defined quantity of interest. In particular, the use of the DWR approach allows for the separation of the discretization error and the quadrature error. Both concepts of error control can be used to steer adaptive schemes for local mesh refinements. In several numerical experiments the performance of the error controls and the adaptive schemes is demonstrated.