Inertial sensors based on micro-electromechanical systems (MEMS) technology, such as accelerometers and angular rate sensors, are cost-effective solutions used in inertial navigation systems in a broad spectrum of applications that estimate position, velocity and orientation of a system with respect to an inertial reference frame. The task of an orientation filter is to compute an optimal solution for the attitude state, consisting of roll, pitch and yaw, through the fusion of angular rate, accelerometer, and magnetometer measurements. The aim of this paper is threefold: first, it serves researchers and practitioners in the signal processing community seeking the most appropriate attitude estimators that fulfills their needs, shedding light on the drawbacks and the advantages of a wide variety of designs. Second, it serves as a survey and tutorial for existing estimator designs in the literature, assessing their design aspects and components, and dissecting their hidden details for the benefit of researchers. Third, a comprehensive list of algorithms is discussed for a fully functional inertial navigation system, starting from the navigation equations and ending with the filter equations, keeping in mind their suitability for power limited embedded processors. The source code of all algorithms is published, with the aim of it being an out-of-box solution for researchers in the field. The reader will take away the following concepts from this article: understand the key concepts of an inertial navigation system; be able to implement and test a complete stand alone solution; be able to evaluate and understand different algorithms; understand the trade-offs between different filter architectures and techniques; and understand efficient embedded processing techniques, trends and opportunities.