In 1970s S.Newhouse discovered that a generic homoclinic bifurcation of a smooth surface diffeomorphism leads to persistent homoclinic tangencies, infinite number of attractors (or repellers), and other unexpected dynamical properties (nowadays called "Newhouse phenomena"). More than 20 years later P.Duarte provided an analog of these results in conservative setting (with attractors replaced by elliptic periodic points). We will discuss these and other recent results on conservative homoclinic bifurcations, and list some related open problems in the field.