许多年前,Rota提出了Rota纲领:找出所有能被(结合)代数上的线性算子满足的代数恒等式.经过一段时间的沉寂之后,近些年来在带算子代数和Gr(o)bner-Shirshov基的观点下,Rota纲领有了快速的进展,发表在一系列从特殊情形到一般情形的论文中.这也表明,Rota的远见卓识可以非常广泛地应用到其他代数结构上,比如李代数和更为广泛的operad.本文介绍了Rota纲领的动机、早期发展及最近在结合代数和李代数上的进展,主要用到了重写系统和Gr(o)bner-Shirshov基的方法.本文回顾了一些老问题,也提出了一些新问题,以推动Rota纲领的进一步发展.“,”Many years ago,Rota proposed a program on determining algebraic identities that can be satisfied by linear operators.After an extended period of dormant,progress on this program picked up speed in recent years,thanks to perspectives from operated algebras and Gr(o)bner-Shirshov bases.These advances were achieved in a series of papers from special cases to more general situations.These perspectives also indicate that Rota\'s insight can be manifested very broadly,for other algebraic structures such as Lie algebras,and further in the context of operads.This paper gives a survey on the motivation,early developments and recent advances on Rota\'s program,for linear operators on associative algebras and Lie algebras.Emphasis will be given to the applications of rewriting systems and Gr(o)bner-Shirshov bases.Problems,old and new,are proposed throughout the paper to prompt further developments on Rota\'s program on algebraic operators.