Massive MIMO (multiple-input multiple-output) is considered as an heir of the multi-user MIMO technology and it has recently gained lots of attention from both academia and industry. By equipping base stations (BSs) with hundreds of antennas, this new technology can provide very large multiplexing gains by serving many users on the same time-frequency resources and thereby bring significant improvements in spectral efficiency (SE) and energy efficiency (EE) over the current wireless networks. The transmit power, pilot training, and spatial transmission resources need to be allocated properly to the users to achieve the highest possible performance. This is called resource allocation and can be formulated as design utility optimization problems. If the resource allocation in Massive MIMO is optimized, the technology can handle the exponential growth in both wireless data traffic and number of wireless devices, which cannot be done by the current cellular network technology. In this thesis, we focus on two resource allocation aspects in Massive MIMO: The first part of the thesis studies if power control and advanced coordinated multipoint (CoMP) techniques are able to bring substantial gains to multi-cell Massive MIMO systems compared to the systems without using CoMP. More specifically, we consider a network topology with no cell boundary where the BSs can collaborate to serve the users in the considered coverage area. We focus on a downlink (DL) scenario in which each BS transmits different data signals to each user. This scenario does not require phase synchronization between BSs and therefore has the same backhaul requirements as conventional Massive MIMO systems, where each user is preassigned to only one BS. The scenario where all BSs are phase synchronized to send the same data is also included for comparison. We solve a total transmit power minimization problem in order to observe how much power Massive MIMO BSs consume to provide the requested quality of service (QoS) of each user. A max-min fairness optimization is also solved to provide every user with the same maximum QoS regardless of the propagation conditions. The second part of the thesis considers a joint pilot design and uplink (UL) power control problem in multi-cell Massive MIMO. The main motivation for this work is that the pilot assignment and pilot power allocation is momentous in Massive MIMO since the BSs are supposed to construct linear detection and precoding vectors from the channel estimates. Pilot contamination between pilot-sharing users leads to more interference during data transmission. The pilot design is more difficult if the pilot signals are reused frequently in space, as in Massive MIMO, which leads to greater pilot contamination effects. Related works have only studied either the pilot assignment or the pilot power control, but not the joint optimization. Furthermore, the pilot assignment is usually formulated as a combinatorial problem leading to prohibitive computational complexity. Therefore, in the second part of this thesis, a new pilot design is proposed to overcome such challenges by treating the pilot signals as continuous optimization variables. We use those pilot signals to solve different max-min fairness optimization problems with either ideal hardware or hardware impairments.