COPENHAGEN — On April 30, 1983, the co-founder and celebrated choreographer of New York City Ballet, George Balanchine, died. Balanchine was his form’s Picasso, the greatest choreographer of the 20th century, who changed the techniques and perceptions of his art. A successor seemed impossible, but a successor there had to be. It was Peter Martins, the tall, blond Danish dancer who had joined City Ballet 13 years earlier.

When the company opens its spring season on April 30, the occasion will mark both Balanchine’s death and 30 years of Mr. Martins’s stewardship of City Ballet and its allied School of American Ballet. This makes him not just one of the longest-serving ballet directors in the United States, but one of the longest-serving directors of any major arts organization in the country.

After three decades, Mr. Martins has much to boast about. The company is financially far more secure, with a $164 million endowment, than it was in Balanchine’s day. The Balanchine and Jerome Robbins repertory has been maintained, with a dizzyingly large number of them performed every season. Musical standards are high, and the current crop of principal dancers includes some of the most remarkable performers in dance. The company commissions more ballets each year than any other major troupe in the world.

Nonetheless, Mr. Martins’s tenure has been stormy. After a honeymoon period following Balanchine’s death, a cold front set in. Mr. Martins was — and still is — ruthlessly criticized for failing to maintain Balanchinian style (a “catastrophically swift decline,” Arlene Croce wrote in The New Yorker in 1993); for not bringing in former dancers to coach; and for programming too many dull ballets of his own.