This article describes a new way of controlling robots using soft tactile sensors: pose-based tactile servo (PBTS) control. The basic idea is to embed a tactile perception model for estimating the sensor pose within a servo control loop that is applied to local object features such as edges and surfaces. PBTS control is implemented with a soft curved optical tactile sensor (the BRL TacTip) using a convolutional neural network trained to be insensitive to shear. In consequence, robust and accurate controlled motion over various complex 3D objects is attained. First, we review tactile servoing and its relation to visual servoing, before formalising PBTS control. Then, we assess tactile servoing over a range of regular and irregular objects. Finally, we reflect on the relation to visual servo control and discuss how controlled soft touch gives a route towards human-like dexterity in robots.