  A review of a recent method is presented to construct certain exact solutions
to the focusing nonlinear Schr\"odinger equation on the line with a cubic
nonlinearity. With motivation by the inverse scattering transform and help from
the state-space method, an explicit formula is obtained to express such exact
solutions in a compact form in terms of a matrix triplet and by using matrix
exponentials. Such solutions consist of multisolitons with any multiplicities,
are analytic on the entire $xt$-plane, decay exponentially as $x\to\pm\infty$
at each fixed $t,$ and can alternatively be written explicitly as algebraic
combinations of exponential, trigonometric, and polynomial functions of the
spatial and temporal coordinates $x$ and $t.$ Various equivalent forms of the
matrix triplet are presented yielding the same exact solution.
