The nanoscale contacts, which play a key role in nanotechnology and micro-/nanoelectromechanical systems, are fundamentally important for a wide range of problems including adhesion, contact formation, friction and wear, etc. Because continuum contact mechanics has limitations when it is applied at length of nanoscale, molecular dynamics (MD) simulations, which can investigate internal physical mechanisms of nanostructures by atomic motions in detail, become one of the most promising approaches for investigating mechanical behaviors of contacts in nanoscale. First, contacts between rigid cylindrical probes with different radii and an elastic half-space substrate are studied by using MD simulations with the assistance of the classical Lennard-Jones potential. For contacts without adhesion, the relationship between the applied force and the contact half-width is analyzed. The von Mises stress distributions are then discussed. For contacts with adhesion, the phenomena of the jump-to-contact, the break-off contact, and the hysteresis are observed. The pressure distributions and the von Mises stress contours in the contact region agree with the existing solutions. Second, the effects of the surface topography on adhesive contacts are studied by using MD simulations with the embedded atom method potential. The adhesive contact mechanical characteristic of a series of asperities with different shapes, different sizes, and different numbers on contacting surfaces are discovered and compared. The results show that the surface topography is one of the major factors, which may influence the contact behaviors between the interfaces of nanoscale components.