Simple microneedle devices for delivery of drugs across or into biological tissue are provided, which permit drug delivery at clinically relevant rates across or into skin or other tissue barriers, with minimal or no damage, pain, or irritation to the tissue. The devices include a substrate to which a plurality of hollow microneedles are attached or integrated, and at least one reservoir, containing the drug, selectably in communication with the microneedles, wherein the volume or amount of drug to be delivered can be selectively altered. The reservoir can be formed of a deformable, preferably elastic, material. The device typically includes a means, such as a plunger, for compressing the reservoir to drive the drug from the reservoir through the microneedles, In one embodiment, the reservoir is a syringe or pump connected to the substrate.