Task-parameterized models of movements aims at automatically adapting movements to new situations encountered by a robot. The task parameters can for example take the form of positions of objects in the environment, or landmark points that the robot should pass through. This tutorial aims at reviewing existing approaches for task-adaptive motion encoding. It then narrows down the scope to the special case of task parameters that take the form of frames of reference, coordinate systems, or basis functions, which are most commonly encountered in service robotics. Each section of the paper is accompanied with source codes designed as simple didactic examples implemented in Matlab with a full compatibility with GNU Octave, closely following the notation and equations of the article. It also presents ongoing work and further challenges that remain to be addressed, with examples provided in simulation and on a real robot (transfer of manipulation behaviors to the Baxter bimanual robot). The repository for the accompanying source codes is available at http://www.idiap.ch/software/pbdlib/.