Non-orthogonal multiple access (NOMA) has received tremendous attention for the design of radio access techniques for fifth generation (5G) wireless networks and beyond. The basic concept behind NOMA is to serve more than one user in the same resource block, e.g., a time slot, subcarrier, spreading code, or space. With this, NOMA promotes massive connectivity, lowers latency, improves user fairness and spectral efficiency, and increases reliability compared to orthogonal multiple access (OMA) techniques. While NOMA has gained significant attention from the communications community, it has also been subject to several widespread misunderstandings, such as $``\textit{NOMA is based on allocating higher power to users with worse channel conditions. As such, cell-edge users receive more power in NOMA and due to this biased power allocation toward cell-edge users inter-cell interference is more severe in NOMA compared to OMA. NOMA also compromises security for spectral efficiency.}''$ The above statements are actually false, and this paper aims at identifying such common myths about NOMA and clarifying why they are not true. We also pose critical questions that are important for the effective adoption of NOMA in 5G and beyond and identify promising research directions for NOMA, which will require intense investigation in the future.