  We study the smoothness and the norm attainment of bounded bilinear operators
between Banach spaces, using the concepts of Birkhoff-James orthogonality and
semi-inner-products. In the finite-dimensional case, we characterize
Birkhoff-James orthogonality of bilinear operators in terms of the norm
attainment set. This yields a nice characterization of smoothness of bilinear
operators between Banach spaces, in the finite-dimensional case. Without any
restriction on the dimension of the space, we obtain a complete
characterization of the norm attainment set of a bounded bilinear operator
using semi-inner-products, which is particularly useful when the concerned
Banach spaces are smooth.
