Stratified spaces appear naturally in singularity theory. Their study relies on invariants, such as intersection cohomology, which are not invariant under all homotopies, rather they are only invariant under homotopies that "preserve" the stratification. Considering stratified objects in a simplicial context, those stratified homotopies lead to the definition of a model category of stratified spaces. In particular, new invariants for stratified spaces can be constructed: the filtered homotopy groups. One can show that these invariants completely characterize stratified weak equivalences, through a stratified version of Whitehead Theorem.