NOVELTY - Structure comprises microstructured anodically active material layers (30, 31) including fibrous or porous anodically active material and having surface that is perpendicular to reference plane, with 1 mu m thickness, 50 mu m height, and void volume fraction of about 0.1, where lineal distance between at least two layers, measured in direction parallel to the reference plane, is greater than the maximum value of height for the layers.    USE - In energy storage device such as batteries, fuel cells, and electrochemical capacitors, for lithium ion batteries for portable electronics e.g. mobile phone and computer.    ADVANTAGE - The present three-dimensional energy storage device can provide a higher rate of energy retrieval than two-dimensional energy storage devices for specific amount of energy stored, such as by minimizing or reducing transport distances for electron and ion transfer between anode and cathode. The device can be more suitable for miniaturization and for applications where geometrical area available for device is limited and/or where energy density requirement is higher than what may be achieved with laminar device.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) electrochemical stack for use in energy storage device, comprising, in a stacked arrangement, cathode structures (26), anode structures (24), and separator layers disposed between anode and cathode structures, the direction of stacking of cathode structures, separator layers, and anode structures is parallel to reference plane, where the anode structures comprise microstructured anodically active material layers;    (2) energy storage device comprising carrier ions, non-aqueous electrolyte and electrochemical stack, where carrier ions are lithium, sodium or potassium ions; and    (3) secondary battery comprising carrier ions, non-aqueous electrolyte and at least two electrochemical stacks.    DESCRIPTION OF DRAWING(S) - The figure shows schematic diagram of two cells of three-dimensional energy storage device.    Cell (22) Base (20)    Anode structure (24)    Cathode structure (26)    Anodically active material layers (30, 31)