Training a neural network with a large labeled dataset is still a dominant paradigm in computational histopathology. However, obtaining such exhaustive manual annotations is often expensive, laborious, and prone to inter and intra-observer variability. While recent self-supervised and semi-supervised methods can alleviate this need by learning unsupervised feature representations, they still struggle to generalize well to downstream tasks when the number of labeled instances is small. In this work, we overcome this challenge by leveraging both task-agnostic and task-specific unlabeled data based on two novel strategies: (i) a self-supervised pretext task that harnesses the underlying multi-resolution contextual cues in histology whole-slide images to learn a powerful supervisory signal for unsupervised representation learning; (ii) a new teacher-student semi-supervised consistency paradigm that learns to effectively transfer the pretrained representations to downstream tasks based on prediction consistency with the task-specific unlabeled data. We carry out extensive validation experiments on three histopathology benchmark datasets across two classification and one regression based tasks, i.e., tumor metastasis detection, tissue type classification, and tumor cellularity quantification. Under limited-label data, the proposed method yields tangible improvements, which is close to or even outperforming other state-of-the-art self-supervised and supervised baselines. Furthermore, we empirically show that the idea of bootstrapping the self-supervised pretrained features is an effective way to improve the task-specific semi-supervised learning on standard benchmarks. Code and pretrained models are made available at: https://github.com/srinidhiPY/SSL_CR_Histo.