An energy storage device comprising carrier ions, a non-aqueous electrolyte and an electrochemical stack, the carrier ions being lithium, sodium or potassium ions, the electrochemical stack comprising, in a stacked arrangement, cathode structures, separator layers and a population of anode structures having a height, HA, of at least 50 micrometers measured in a direction orthogonal to a reference plane, the separator layers being disposed between the anode structures and the cathode structures, the direction of stacking of the cathode structures, the separator layers, and the anode structures being parallel to the reference plane, each member of the population of anode structures comprising a microstructured anodically active material layer having a front surface, a back surface, a thickness, T, measured from the front surface to the back surface, and a void volume fraction of at least 0.1, the front and back surfaces being substantially perpendicular to the reference plane, the thickness, T, being at least 1 micrometer and measured in a direction parallel to the reference plane, the microstructured anodically active material layers comprising a fibrous or a porous anodically active material oriented such that (i) anodically active material fibers comprised by the microstructured material layers are attached to the back surface of the layers and predominantly have central axes that are substantially parallel to the reference plane at the point of attachment of the fibers to the back surfaces of the microstructured anodically active material layers, and (ii) the pores of porous anodically active material comprised by the microstructured material layers predominantly have major axes that are substantially parallel to the reference plane wherein the lineal distance, DL, between at least two members of the population, measured in a direction parallel to the reference plane, is greater than the maximum value of HA for the population.