We probe the transitions between solid-like and fluid-like granular states in the presence of shaking in the horizontal and vertical directions. These transitions are fundamental to other aspects of granular flow such as avalanche flow, in which there is a free surface. Key control parameters include accelerations in the vertical and horizontal directions, Γ i = A i ω2 i /g, for shaking of the form s i = A i cos(ω i t + φ i ), i = h, v. Here, g is the acceleration of gravity. Also important is the relative phase between the two modes of shaking. We focus on low to moderate dimensionless accelerations, 0 < Γ v,h < 1.6. We consider first the case Γ v = 0, i.e. pure horizontal shaking. In this case, there is a hysteretic transition between solid and fluid states, where the fluid state consists of a sloshing layer of material of height H plus additional transverse flow. The hysteresis is lifted in the presence of a modest amount of fluidization by gas flow, or if a slight overburden is provided. We also identify a time scale, τ, for the transition between the phases that diverges inversely as the distance ε = (Γ h –Γ hc )/Γ hc , from the appropriate transition points, i.e. as τ α ε-1. We identify a new convective mechanism, associated with horizontal shearing at the walls, as the mechanism that drives the transverse convective flow. For combined horizontal and vertical shaking, there exist a related set of novel dynamics and stability properties. These include the spontaneous formation of a static heap and a transition to flow, similar to the flow state under horizontal shaking, when the vertical acceleration Γ v < 1. A simple friction model provides a good description of the steady states and a reasonably good description of the transition to flow. Horizontal and vertical shaking frequencies that differ by a small amount can lead to a novel switching state, as the relative phase, φ h —φ v , shifts over time.