This paper elaborates on the design challenges, opportunities, and solutions for New Radio-based access to Unlicensed spectrum (NR-U) by taking into account the beam-based transmissions and the worldwide regulatory requirements. NR-U intends to expand the applicability of 5th generation New Radio access technology to support operation in unlicensed bands by adhering to Listen-Before-Talk (LBT) requirements for accessing the channel. LBT was already adopted by different variants of 4th generation Long Term Evolution (LTE) in unlicensed spectrum, i.e., Licensed-Assisted Access and MulteFire, to guarantee fair coexistence among different radio access technologies. In the case of beam-based transmissions, the NR-U coexistence framework is significantly different as compared to LTE in unlicensed spectrum due to the use of directional antennas, which enhance the spatial reuse but also complicate the interference management. In particular, beam-based transmissions are needed in the unlicensed spectrum at millimeter-wave (mmWave) bands, which is an attractive candidate for NR-U due to its large amount of allocated spectrum. As a consequence, some major design principles need to be revisited to address coexistence for beam-based NR-U. In this paper, different problems and the potential solutions related to channel access procedures, frame structure, initial access procedures, re-transmission procedures, and scheduling schemes are discussed. A simulation evaluation of different LBT-based channel access procedures for NR-U/Wi-Fi indoor mmWave coexistence scenarios is also provided.