Cell-free Massive MIMO is considered as a promising technology for satisfying the increasing number of users and high rate expectations in beyond-5G networks. The key idea is to let many distributed access points (APs) communicate with all users in the network, possibly by using joint coherent signal processing. The aim of this paper is to provide the first comprehensive analysis of this technology under different degrees of cooperation among the APs. Particularly, the uplink spectral efficiencies of four different cell-free implementations are analyzed, with spatially correlated fading and arbitrary linear processing. It turns out that it is possible to outperform conventional Cellular Massive MIMO and small cell networks by a wide margin, but only using global or local minimum mean-square error (MMSE) combining. This is in sharp contrast to the existing literature, which advocates for maximum-ratio combining. Also, we show that a centralized implementation with optimal MMSE processing not only maximizes the SE but largely reduces the fronthaul signaling compared to the standard distributed approach. This makes it the preferred way to operate Cell-free Massive MIMO networks. Non-linear decoding is also investigated and shown to bring negligible improvements. ). same time-frequency resource [8]. The characteristic feature of mMIMO, compared to traditional multi-user MIMO, is that each BS has many more antennas than UEs in the cell. Signal processing methods, such as minimum mean-squared error (MMSE) combining in the uplink, can be used individually at each BS to suppress interference from both the same and other cells [3], [9], [10], without the need for any BS cooperation. The mMIMO theory also supports deployments with spatially distributed arrays in each cell [11], [12], as also illustrated in Fig. 1(a). This setup is essentially the same as the Distributed Antenna System (DAS) setup in [13] and Coordinated Multi-Point (CoMP) with static, disjoint cooperation clusters [14], [15]. These are all different embodiments of cellular networks.An alternative network infrastructure was considered in [16], [17] under the name of Cell-free mMIMO. The idea is to deploy a large number of distributed single-antenna access points (APs), which are connected to a central processing unit (CPU), also known as an edge-cloud processor [18] or C-RAN (cloud radio access network) data center [19]. The CPU operates the system in a Network MIMO fashion, with no cell boundaries, to jointly serve the UEs by coherent joint transmission and reception [15], [20]-[23]. Compared to traditional Network MIMO, the outstanding aspect of Cellfree mMIMO is the operating regime with many more APs than UEs [16]. From an analytical perspective, an important novelty was that imperfect channel state information (CSI) was considered in the performance analysis, while perfect CSI was often assumed in the past [15]. The paper [16] advocated the use of maximum ratio (MR) processing (a.k.a. matched filtering or conjugate beamforming) locally at each AP, whil...