  Brief introduction to the discrete quantum mechanics is given together with
the main results on various exactly solvable systems. Namely, the intertwining
relations, shape invariance, Heisenberg operator solutions,
annihilation/creation operators, dynamical symmetry algebras including the
$q$-oscillator algebra and the Askey-Wilson algebra. A simple recipe to
construct exactly and quasi-exactly solvable Hamiltonians in one-dimensional
`discrete' quantum mechanics is presented. It reproduces all the known ones
whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal
polynomials of a continuous or a discrete variable. Several new exactly and
quasi-exactly solvable ones are constructed. The sinusoidal coordinate plays an
essential role.
