Global bifurcations are frequently encountered in the dynamic behavior of chemically reacting systems and their models. They cause dramatic qualitative changes in the system response, such as the birth and death of oscillations and even the onset of chaos. They involve entire regions of the system phase space, and due to their nature they are in general not predictable by standard local bifurcation methods, analytical or numerical. Special methods and algorithms must therefore be developed to locate and analyze them in parameter space. This paper presents such methods and algorithms and illustrates them through standard chemical engineering examples. Test cases include lumped chemical reactor models (homogeneous and heterogeneous, autonomous and periodically forced), a problem of compressible gas flow in porous media, and a case of two coupled oscillators. The phenomena discussed include infinite-period bifurcations, saddle connections, frequency locking, and the creation and extinction of multifrequency responses through global manifold interactions (homoclinic tangles).