CubeSats are a type of small satellites (< 500 kg) that weigh several kilograms and consist of multiple Units (U) measuring 100 × 100 × 113.5 mm3. CubeSats emerged as a low-cost alternative to conventional large satellites, and have since demonstrated capabilities for communication, Earth observation, technology demonstration and many other. The primary goal of CubeSats, as it is the case with any miniaturized satellite, is to reduce the cost of orbital deployment. CubeSats are commonly launched as a secondary payload on large launch vehicles. One or several satellites are placed in a dedicated deployment system, which typically accommodates three CubeSat Units. The deployment system strictly limits the dimensions of any features on the CubeSat surface. CubeSat antennas perform the same functions as antennas on conventional satellites, such as telemetry and command, communication, navigation or inter-satellite links (ISL). However, most traditional antennas for small satellites are not suitable for CubeSats due to the profile constraints of the deployment system. Two approaches for antenna design are generally adopted. In the first, one or several low-profile antennas are placed on the CubeSat exterior. In the second, deployable antenna structures are used if the CubeSat platform does not offer sufficient dimensions. At low frequencies, the additional space is required to achieve a good radiation efficiency, whereas at high frequencies an increased antenna aperture provides a high gain. This thesis describes several antenna geometries, both low-profile and deployable, which enable several communication aspects of an Internet-of-Things (IoT) constellation of 3U CubeSats in the Low Earth Orbit (LEO). The main novelty of the proposed solutions is in their electromagnetic performance, as opposed to most CubeSat antenna designs where the mechanical design is the main achievement. The presented antennas succeed to exhibit a wide bandwidth or a specified radiation under strict size constraints. The thesis presents several wideband aperture-coupled patch antennas for TT&C and data downlink in S and X bands. A thoroughly investigated shielded-stripline feeding structure enables a wideband circular polarization (CP) with a unidirectional radiation, and demonstrates capabilities such as interference suppression of adjacent frequencies and efficient CubeSat integration. Patch-antenna arrays in L band are then presented, which radiate several independent beams for the capacity increase of an IoT machine-to-machine (M2M) communication system. The high permittivity of the antenna substrates lead to a strong coupling to the 3U CubeSat structure, emphasizing the importance of the antenna placement. Finally, different configurations of high-gain fixed-beam reflectarrays (RA) and transmitarrays (TA) are for the first time proposed for CubeSat ISL LEO communications in K band. Two novel unit cells are presented for RA and TA antennas, based on coupled loops and aperture-coupled patches, respectively. An axially corrugated CP horn antenna is designed as the feeding element for the arrays. A prototype of this antenna is fabricated using additive manufacturing in aluminum. The performance of all antennas, presented in this thesis, is validated by agreements between the calculation and 3D-simulation results and the VNA and anechoic-chamber measurements of several prototypes.