  Ideals generated by adjacent 2-minors are studied. First, the problem when
such an ideal is a prime ideal as well as the problem when such an ideal
possesses a quadratic Gr\"obner basis is solved. Second, we describe explicitly
a primary decomposition of the radical ideal of an ideal generated by adjacent
2-minors, and challenge the question of classifying all ideals generated by
adjacent 2-minors which are radical ideals. Finally, we discuss connectedness
of contingency tables in algebraic statistics.
