Over the last years many efforts have been focused to develop concentrated solar energy technologies. On the other hand, nonimaging optical devices such as Dielectric Totally Internally Reflecting Concentrators (DTIRCs) stand out for their high concentration and homogeneous radiant flux on the spot of the receiver of the concentrator. In this work we reformulate the original formulation of DTIRCs to obtain an analytical framework for feasible designs which are easily implemented for computer numerical control (CNC) manufacturing. Additionally we extend the formulation to aspherical front surfaces, such as Parabolic Dielectric Totally Internally Reflecting Concentrators (PDTIRC) and Elliptic Dielectric Totally Internally Reflecting Concentrators (EDTIRCs), and discuss their most relevant features for concentrated solar applications.