A graph whose edges are labeled either as positive or negative is called a signed graph. Motivated from the seminal paper of B. D. Acharya on domination in signed graphs, we in this article, provide answers to some of the problems in that paper and define open domination for a signed graph and its open domination number. We analyze this notion for certain classes of signed graphs and also give exact values for their open domination numbers. We also discuss about certain bounds for the open domination number of a signed graph.