In this paper, we study the capacity of multiple-input multiple-output (MIMO) systems under the constraint that amplitude-limited inputs are employed. We compute the channel capacity for the special case of multiple-input singleo-utput (MISO) channels, while we are only able to provide upper and lower bounds on the capacity of the general MIMO case. The bounds are derived by considering an equivalent channel via singular value decomposition, and by enlarging and reducing the corresponding feasible region of the channel input vector, for the upper and lower bounds, respectively. We analytically characterize the asymptotic behavior of the derived capacity upper and lower bounds for high and low noise levels, and study the gap between them. We further provide several numerical examples illustrating their computation.