In order to determine the orbital symmetry of the superconducting order parameter (OP) in the high temperature superconducting compounds (HTSC), an experiment must be able to distinguish the superconducting gap from the nonsuperconducting pseudogap. Furthermore, only a phase-sensitive experiment can distinguish a highly anisotropic s-wave OP from one of different symmetry, such as the popular d,2,2-wave OP. A closely related issue is the coherence of the c-axis tunnelling in'the HTSC. In this review, we describe the present state of the most reliable phase-sensitive tests of OP symmetry in any superconductor: the c-axis twist experiments in Bi2Sr2CaCU2O818 (Bi2212). We also present and discuss the data relevant for the related question of the c-axis tunnelling coherence in Bi2212. There are presently three c-axis twist experiments on Bi2212: the bicrystal experiments (Li et al., Phys. Rev. Lett. 83 4160 (1999)), the artificial cross-whisker experiments (Takano et al., Phys. Rev. B 65 140513 (2002)), and the natural cross-whisker experiments (Latyshev et al., Phys. Rev. B 70 094517 (2004)). We then summarize the extensive theoretical analyses of the possible implications, so that reliable conclusions can be inferred. Included in the theoretical discussion are an introduction, the twist theorem for weak, first-order c-axis tunnelling between two d-wave superconducting layers twisted 45' about the c-axis, treatments of weak, first-order c-axis tunnelling matrix elements with varying amounts of coherent and incoherent components, and effects of the Fermi surface, strong coherent tunnelling, orthorhombicity, nanoscale disorder, and OP twisting near the physical twist junction. It is shown that all three experiments can only be understood in terms of a substantial s-wave OP component for T < Tc. The bicrystal and natural cross-whisker experiments are also consistent with the preponderance of other data that the c-axis tunnelling is strongly incoherent.In order to determine the orbital symmetry of the superconducting order parameter (OP) in the high temperature superconducting compounds (HTSC), an experiment must be able to distinguish the superconducting gap from the non-superconducting pseudogap. Furthermore, only a phase-sensitive experiment can distinguish a highly anisotropic s-wave OP from one of different symmetry, such as the popular d(x)2(-y)2-wave OP. A closely related issue is the coherence of the c-axis tunnelling in the HTSC. In this review, we describe the present state of the most reliable phase-sensitive tests of OP symmetry in any superconductor: the c-axis twist experiments in Bi2Sr2CaCu2O8+delta (Bi2212). We also present and discuss the data relevant for the related question of the c-axis tunnelling coherence in Bi2212. There are presently three c-axis twist experiments on Bi2212: the bicrystal experiments (Li et al., Phys. Rev. Lett. 83 4160 (1999)), the artificial cross-whisker experiments (Takano et al., Phys. Rev. B 65 140513 (2002)), and the natural cross-whisker experiments (Latyshev et al., Phys. Rev. B 70 094517 (2004)). We then summarize the extensive theoretical analyses of the possible implications, so that reliable conclusions can be inferred. Included in the theoretical discussion are an introduction, the twist theorem for weak, first-order c-axis tunnelling between two d-wave superconducting layers twisted 45 degrees about the c-axis, treatments of weak, first-order c-axis tunnelling matrix elements with varying amounts of coherent and incoherent coponents, and effects of the Fermi surface, strong coherent tunnelling, orthorhombicity, nanoscale disorder, and OP twisting near the physical twist junction. It is shown that all three experiments can only be understood in terms of a substantial s-wave OP component for T <= T-c. The bicrystal and natural cross-whisker experiments are also consistent with the preponderance of other data that the c-axis tunnelling is strongly incoherent.
