The demand to achieve higher data-rates and support increasing data-traffic in wireless systems is driving the exploration of the underutilized millimeter wave (mmWave) spectrum for future communication systems. This has led to the development of fifth generation (5G) cellular standards and Wi-Fi standards such as 802.11ad, 802.11ay, etc. The higher frequency bands enable massive Multiple-Input Multiple-Output (MIMO) implementations within small form-factors. However, excessive cost, signal processing complexity and hardware constraints pose challenges in implementing fully digital/analog (homogeneous) beamforming schemes. Hybrid beamforming architectures can be employed to overcome these challenges and meet the performance of homogeneous schemes in mmWave systems. The goal of this thesis is to design, implement and analyze hybrid beamforming schemes to overcome the limitations of high frequency mmWave spectrum. The first stage involves implementation of digital precoding for codebook-based limited-feedback systems. The precoder matrices are chosen from 4G LTE codebooks. To obtain high data-rates, spectral efficiency, low latency and reliable communication, technologies such as Orthogonal Frequency Division Multiplexing (OFDM), MIMO, channel coding using Turbo Codes and Low-Density Parity-Check (LDPC) Codes, modulation schemes such as M-ary (M = 4, 16, 64, 256) Quadrature Amplitude Modulation (QAM) are used in the simulation platform. The bit error rate (BER) performance is analyzed for various scenarios in frequency selective fading and flat fading channel models. The second stage involves implementation of analog beamforming using phased-array antennas. For analog beam selection, methods such as exhaustive search, side-to-side search, and iterative search methods are studied. An extended Saleh-Valenzuela geometric model is implemented to emulate the mmWave channel. The final stage involves the design and implementation of hybrid beamforming schemes by combining the digital and analog stages. For performance analysis, two beamforming code-books: Angle-of-Arrival/Angle-of-Departure (AoA/AoD) codebook and Quantized RF code-book are used in the hybrid design. The BER performance of the system is compared using exhaustive and side-to-side search methods. The designed hybrid scheme achieves the BER performance close to the optimal fully digital scheme using AoA/AoD codebook and achieves near-optimal performance using RF codebook. All algorithms designed are implemented using the MATLAB R2018a simulation platform.