Limit[expr, x->x0, Direction->1] computes the limit as x approaches from smaller values. Limit[expr, x->x0, Direction->-1] computes the limit as x approaches from larger values.
Limit returns Interval objects to represent ranges of possible values, for example at essential singularities.
Limit returns unevaluated when it encounters functions about which it has no specific information. Limit therefore by default makes no explicit assumptions about symbolic functions.
Assumptions can be specified as a setting for the option Assumptions.
Limit uses the setting Direction->Automatic, which determines the direction from assumptions that have been given, using Direction as the default. For limit points at infinity, the direction is determined from the direction of the infinity.