We briefly review growth models and related continuum equations propos
ed for describing epitaxial growth. We mainly consider conservative gr
owth without desorptions and vacancies under chemical-bonding environm
ent. We also speculate on the asymptotic behaviors of growth models an
d the correspondence between the models and continuum equations. Next,
we investigate a growth model, a natural extension of the Wolf-Villai
n model, which is shown to be described by the most general continuum
equation up to fourth order for a conservative growth. Numerical simul
ations on one-dimensional and two-dimensional substrates show crossove
r behaviors of growth exponents according to the continuum equation.