Water is the most abundant substance on Earth, and its liquid properties are distinct from those of other fluids, posing a challenge for in silico simulations not only of condensed water but also of aqueous chemistry. In this work, we explored the performance of Minnesota meta-GGA and hybrid meta-GGA density functionals in describing the structure and dynamics of liquid water via ab initio molecular dynamics simulations. Contrary to the prevailing belief that local and semilocal functionals overstructure water, leading to underestimation of dynamical properties, the Minnesota meta-GGAs exhibit the opposite trend. M06-L, revM06-L, and M11-L lead to understructuring of water, while MN12-L and MN15-L lack cohesive effects, resulting in increased intermolecular distances. This behavior can be attributed to the weakening of the hydrogen bond network causing dynamical fingerprints that are far too fast. On the other hand, while most of the hybrid Minnesota functionals remain understructured (M06, M08-HX, M08-SO, M11, MN12-SX, MN15), their dynamical properties generally improve over those obtained with local and semilocal functionals. The inclusion of exact exchange was identified as a key ingredient for the correct description of hydrogen bonds leading to improved structural and dynamical properties. In contrast, we found that an excessive amount of exact exchange (M06-HF) shortens and strengthens the hydrogen bonds between molecules, thus giving water properties that are too glassy.