Aptamers are short single-stranded DNA or RNA, which can be selected from random combinatorial library by SELEX in vitro. The SELEX technology has been modified over the years in different ways to become more efficient and less time-consuming, to reach higher affinities of the aptamers and for automation of the process. The multitude of different targets used in SELEX implicates aptamers are possible to be selected using any target theoretically. This paper presents the SELEX technology screening aptamers and its latest progress including modified selection methods (negative SELEX, counter SELEX and substractive SELEX) and efficient selection methods (CE-SELEX, non-SELEX, automated-SELEX and microfluidic SELEX). Additionally, cell SELEX using whole cells as targets is introduced. Varieties of live pathogenic organisms and many cancer cells have been used as targets for cell SELEX. Finally, an overview of biomedical applications of aptamers is given. Aptamers as a class of biorecognition elements that possess many advantages such as high specificity and binding affinity, easy synthesis, easy modification, small size, non-toxicity and good stability, have been increasingly applied in biomedical field. Especially, the combination of aptamers with nanomaterials will continuously play more and more important roles in many applications such as detection of targets, diagnosis and treatment of diseases, bioimaging, and drugs delivery.