Speech processing for under-resourced languages is an active field of research, which has experienced significant progress during the past decade. We propose, in this paper, a survey that focuses on automatic speech recognition (ASR) for these languages. The definition of under-resourced languages and the challenges associated to them are first defined. The main part of the paper is a literature review of the recent (last 8 years) contributions made in ASR for under-resourced languages. Examples of past projects and future trends when dealing with under-resourced languages are also presented. We believe that this paper will be a good starting point for anyone interested to initiate research in (or operational development of) ASR for one or several under-resourced languages. It should be clear, however, that many of the issues and approaches presented here, apply to speech technology in general (text-to-speech synthesis for instance).