Unlike their underlying bulk solid, surfaces begin to disorder well below the bulk melting temperature. This disorder gives rise to several new continuous phase transitions. Two of them will be reported here: surface roughening and surface melting. Surface roughening can be characterized by a divergence of the interfacial width as the crystal size goes to infinity, or, equivalently, by the logarithmic growth of the height-height correlations at long distance for a thermodynamically large sample. This phenomena has dramatic consequences on crystal shapes, crystal growth rates, ... Surface melting, which usually occurs at higher temperatures (but always below the triple point), involves the occurrence of a mobile film that wets the solid-vapor interface. The thickness of the liquid-like film diverges as the melting temperature is approached. Recent observations on surface melting are discussed and the implications of this surface disordering on crystal growth phenomena are reviewed.