Existing video instance segmentation (VIS) approaches generally follow a closed-world assumption, where only seen category instances are identified and spatio-temporally segmented at inference. Open-world formulation relaxes the close-world static-learning assumption as follows: (a) first, it distinguishes a set of known categories as well as labels an unknown object as 'unknown' and then (b) it incrementally learns the class of an unknown as and when the corresponding semantic labels become available. We propose the first open-world VIS approach, named OW-VISFormer, that introduces a novel feature enrichment mechanism and a spatio-temporal objectness (STO) module. The feature enrichment mechanism based on a light-weight auxiliary network aims at accurate pixel-level (unknown) object delineation from the background as well as distinguishing category-specific known semantic classes. The STO module strives to generate instance-level pseudo-labels by enhancing the foreground activations through a contrastive loss. Moreover, we also introduce an extensive experimental protocol to measure the characteristics of OW-VIS. Our OW-VISFormer performs favorably against a solid baseline in OW-VIS setting. Further, we evaluate our contributions in the standard fully-supervised VIS setting by integrating them into the recent SeqFormer, achieving an absolute gain of 1.6% AP on Youtube-VIS 2019 val. set. Lastly, we show the generalizability of our contributions for the open-world detection (OWOD) setting, outperforming the best existing OWOD method in the literature. Code, models along with OW-VIS splits are available at https://github.com/OmkarThawakar/OWVISFormer.