The rapid control of surface attachment is a key feature of natural adhesive systems used for locomotion, and a property highly desirable for man-made adhesives. Here, we describe the challenges of adhesion control and the timescales involved across diverse biological attachment systems and different adhesive mechanisms. The most widespread control principle for dynamic surface attachment in climbing animals is that adhesion is 'shear-sensitive' (directional): pulling adhesive pads towards the body results in strong attachment, whereas pushing them away from it leads to easy detachment, providing a rapid mechanical 'switch'. Shear-sensitivity is based on changes of contact area and adhesive strength, which in turn arise from non-adhesive default positions, the mechanics of peeling, pad sliding, and the targeted storage and controlled release of elastic strain energy. The control of adhesion via shear forces is deeply integrated with the climbing animals' anatomy and locomotion, and involves both active neuromuscular control, and rapid passive responses of sophisticated mechanical systems. The resulting dynamic adhesive systems are robust, reliable, versatile and nevertheless remarkably simple. This article is part of the theme issue 'Transdisciplinary approaches to the study of adhesion and adhesives in biological systems'.