Computational work in continuum hypersonics and, in particular, the difficulties encountered during the development of the methods at the DLR Institute for Theoretical Fluid Mechanics are presented. Finite-difference schemes with implicit-explicit central discretisation and shock fitting and with upwind-TVD formulation and shock capturing are discussed. c.g., for strong shock--shock interactions. 3D flows of perfect gas at large angle of attack are considered, including those with radiation-adiabatic surface boundary conditions. 2D or axisymmetric as well as 3D tlows in thermochemical equilibrium are simulated using either the Tannehill curve-fitting approach for air or the minimization procedure for Gibbs' free energy which is more general at the expense of larger cost. Nonequilibrium tlow simulations are discussed for axisymmetric nitrogen and air model tlows. With the help of an appropriate model equation for finite-rate chemistry it is shown that the usual Harten-Yee approach does not allow to propagate shock waves in a time-accurate fashion if large source terms are present.