In this tutorial review we describe the recent progress on catalytic microtubular engines fabricated by rolled-up nanotech on polymers. We summarize the technical aspects of the technology and the basic principles that cause the catalytic microengines to self-propel in fuel solutions. The control over speed, directionality and interactions of the microengines to perform tasks such as cargo transportation is also discussed. We compare this technology to other fabrication techniques of catalytic micro-/nanomotors and outline challenges and opportunities for such engines in future studies. Since rolled-up nanotech on polymers can easily integrate almost any type of inorganic material, huge potential and advanced performance such as high speed, cargo delivery, motion control, and dynamic assembly are foreseen—ultimately promising a practical way to construct versatile and intelligent catalytic tubular microrobots.