  Pattern forming systems allow for a wealth of states, where wavelengths and
orientation of patterns varies and defects disrupt patches of monocrystalline
regions. Growth of patterns has long been recognized as a strong selection
mechanism. We present here recent and new results on the selection of patterns
in situations where the pattern-forming region expands in time. The wealth of
phenomena is roughly organized in bifurcation diagrams that depict wavenumbers
of selected crystalline states as functions of growth rates. We show how a
broad set of mathematical and numerical tools can help shed light into the
complexity of this selection process.
