This Ph.D. dissertation deals with the design of low-voltage analog fractional-order integrated circuits. Fractional-order systems are an emerging area of multidisciplinary research labeled even as the “21st century systems”. Electronic engineers are very interested in applying the concept of fractional calculus. It is motivated mainly by the interdisciplinary nature of this research and possibility to obtain qualitatively new circuit solutions that can provide characteristics not available at integer-order systems. For example, the capability for precise control of the slope of frequency characteristics in fractional-order filters in comparison with the corresponding integer-order filters is an attractive feature. Fractional-order impedance circuits are also very promising in modeling electrical properties of biological materials, tissues or cells. Such element, which exhibits fractional-order impedance properties is known as fractance device. However, there are no commercial fractance devices that make use of the advantages of s^α, integer-order approximations have to be used. For this purpose, the 2nd-order approximation of Continued Fraction Expansion is utilized in order to present a systematic way for describing the design equations of fractional-order generalized transfer functions. To this direction, the design and realization of fractional-order analog integrated circuits offering: (i) capability for on-chip implementation, (ii) capability for low-voltage operation, and (iii) electronic adjustment of their characteristics, is introduced for the first time in the literature. Moreover, they are resistorless realizations, and only grounded capacitors are employed. As a first step, fractional-order differentiator/integrator topologies are introduced, which are able to fulfill the following benefits: (i) capability of being realized using the same topology, (ii) the frequency characteristics as well as the fractional-order α are able to be easily electronically tuned, and (iii) they are fully integratable topologies. Furthermore, fractional-order generalized filters are realized, offering the following characteristics (i) capability of realizing different families of filters (i.e. Butterworth, Chebyshev, etc) using the same topology (ii) capability of realizing different types of filters classified through the form of frequency response (i.e. lowpass, highpass, bandpass, etc) using the same topology. All the above frequency characteristics as well as the fractional-order are able to be easily electronically tuned offering design flexibility and programmability. Also, sampled-data fractional-order filters are also realized for the first time in the literature.The main active cells that are employed are current mirrors, non-linear transconductance cells (known as S, C cells), and Operational Transconductance Amplifiers (OTAs). As a result, the designer has only to choose the appropriate values of the dc bias currents in order to realize the desired transfer function, and, therefore, the proposed schemes offer attractive features.In addition, fully integrated fractional-order (capacitor and inductor) emulators, offering the following attractive benefits: electronic tuning of the impedance, the order, and the bandwidth of operation, are fabricated using the AMS 0.35um CMOS process the efficiency of which is proofed through experimental results.Finally, applications of fractional-order circuits are presented proofing the nessecity of fractional-order calculus, especially when compared with the corresponding integer-order counterparts. Thus, a pre-processing stage suitable for the implementation of the Pan-Tompkins algorithm for detecting the QRS complexes of a noisy electrocardiogram is realized. Also, a fully tunable implementation of the Cole-Cole model used for the modeling of biological tissues is realized. A simple non-impedance based measuring technique for super-capacitors is introduced and this is very important taking into account that the characterization of the parameters of fractional -order circuits is an important procedure, which in general requires an expensive equipment.