Acoustic cloaking has received significant interest due to the appealing ability to render an object acoustically invisible. In a similar concept to acoustic cloaking, acoustic illusions provide the capability to misrepresent the acoustic field of an object. Combining acoustic cloaking and illusions with numerical discretization methods allow objects of greater complexity to be considered. This work presents active acoustic cloaking and illusions of three-dimensional rigid objects. The boundary element method is utilized to efficiently predict the exterior acoustic domain. A multi-input/multi-output control system comprising monopole control sources, error sensors, and a controller based on a feedforward linear-quadratic regulator algorithm is employed. Active acoustic cloaking of a simple object corresponding to a sphere is demonstrated for both non-decaying and decaying incident fields. For the same control configuration but minimizing a cost function based on different error signals, acoustic illusions are generated to mimic the presence of a sphere within a free field. Illusional fields are also generated for a cube and a bird to misrepresent their size or orientation.