We show that the coupling of quantum emitters to a two-dimensional reservoir with a simple band structure gives rise to exotic quantum dynamics with no analogue in other scenarios and which can not be captured by standard perturbative treatments. In particular, for a single quantum emitter with its transition frequency in the middle of the band we predict an exponential relaxation at a rate different from that predicted by the Fermi's Golden rule, followed by overdamped oscillations and slow relaxation decay dynamics. This is accompanied by directional emission into the reservoir. This directionality leads to a modification of the emission rate for few emitters and even perfect subradiance, i.e., suppression of spontaneous emission, for four quantum emitters.The interaction of quantum emitters (QEs) with propagating bosonic particles, e.g., photons, lies at the core of Quantum Optics [1]. This interaction leads, for example, to collective interactions between QEs [2, 3] which can be harnessed for both quantum information and simulation applications. New avenues in the integration of QEs with nanophotonic structures [4][5][6][7][8][9][10][11][12][13][14] provide us with systems in which the QEs interact with low dimensional bosonic modes, with complicated energy dispersions in the case of engineered dielectrics [6][7][8][9][10][11][12]. Despite originally the main motivation of such implementations was to exploit the small sizes to enhance light-matter interactions, it was soon realized that intriguing phenomena arise because of the reduced dimensionality. One particular aspect is the possibility of realizing chiral emission [15][16][17], which can display very uncommon features [18,19]. Another one is the possibility of exploiting the phenomena of sub and superradiance [11,12,[20][21][22], e.g., to enhance the coupling to the emitter [23], to generate QE entanglement [18,24], to produce non-classical light [25,26], or even to perform quantum computation [27].The dynamics of QEs in 1D reservoirs is relatively simple, specially when their transition frequency, ω e , lies within a band. Perturbative treatments predict that a single QE initially excited decays at a rate, Γ, given by the Fermi's Golden Rule (FGR), i.e. proportional to the density of states of the bath at ω e . The emission mostly occurs in the bath modes that are resonant with that frequency. Typically, there are two such modes of associated momentum ±k e , leading to a symmetric left/right emission. When two (or more) QEs are present, the existence of only two such modes leads to super/subradiant states, where the emission is enhanced or suppressed by interference. In higher dimensions for structureless baths, a single QE will also decay at a rate given by the FGR. However, the emission takes place in different directions as there are many resonant modes in the bath. For two QEs, the interference in the emission cannot occur in all those modes at the same time [28] and thus, the phenomena of sub and superradiance are generically absent.In this manus...