As an interesting and emerging topic, co-saliency detection aims at simultaneously extracting common salient objects from a group of images. On one hand, traditional co-saliency detection approaches rely heavily on human knowledge for designing hand-crafted metrics to possibly reflect the faithful properties of the co-salient regions. Such strategies, however, always suffer from poor generalization capability to flexibly adapt various scenarios in real applications. On the other hand, most current methods pursue co-saliency detection in unsupervised fashions. This, however, tends to weaken their performance in real complex scenarios because they are lack of robust learning mechanism to make full use of the weak labels of each image. To alleviate these two problems, this paper proposes a new SP-MIL framework for co-saliency detection, which integrates both multiple instance learning (MIL) and self-paced learning (SPL) into a unified learning framework. Specifically, for the first problem, we formulate the co-saliency detection problem as a MIL paradigm to learn the discriminative classifiers to detect the co-saliency object in the "instance-level". The formulated MIL component facilitates our method capable of automatically producing the proper metrics to measure the intra-image contrast and the inter-image consistency for detecting co-saliency in a purely self-learning way. For the second problem, the embedded SPL paradigm is able to alleviate the data ambiguity under the weak supervision of co-saliency detection and guide a robust learning manner in complex scenarios. Experiments on benchmark datasets together with multiple extended computer vision applications demonstrate the superiority of the proposed framework beyond the state-of-the-arts.