Multiple allotropes and/or chemical compounds can be formed under various pressure / temperature conditions, and some of these could remain metastable under standard conditions for time scales as long as the age of the universe (in fact it is estimated that 50% of all known inorganic compounds are metastable ones!). But the number of known allotropes/compounds pales in comparison with the number of hypothetical ones with energetic feasibility. For any given thermodynamic state, thousands of energetically competitive structures are plausible, a subset of which will exhibit mechanical stability. Further subsets of these structures offer enticing physical properties that differ from those of thermodynamic ground states. Here we delineate thermodynamic and kinetic synthesis methods and discuss strategies and examples for accessing these states experimentally. In particular, we discuss successful experimental realization of new forms of silicon and carbon.