Straight and curved catheters for treatment or diagnoses of tissue, including cardiac tissue, using hydrogel virtual electrodes and hydrogel sensing electrodes are disclosed. Each catheter comprises at least one conductive hydrogel electrode, whether a virtual electrode or a sensing electrode. Hydrogel virtual electrodes may be used to deliver ablative energy or chemotherapeutic agents to tissue. Hydrogel sensing electrodes may be used to map various electrical activity of tissue. The ablation catheters include a variety of hydrogel delivery features to deliver the conductive hydrogel electrodes against or adjacent to tissue to be treated. Each hydrogel delivery feature comprises at least one opening in the distal portion of the catheter and may also include a permeable or semi-permeable membrane. The mapping catheters include conductive hydrogel disks (i.e., conductive hydrogel sensing electrodes) and nonconductive hydrogel disks. Methods of treating and diagnosing tissue using hydrogel virtual electrodes and hydrogel sensing electrodes are also disclosed.