Self-supervised learning (SSL) aims to eliminate one of the major bottlenecks in representation learning - the need for human annotations. As a result, SSL holds the promise to learn representations from data in-the-wild, i.e., without the need for finite and static datasets. Instead, SSL should exploit the continuous stream of data being generated on the internet or by agents exploring their environments. In this work, we investigate whether traditional self-supervised learning approaches would be effective deployed in-the-wild by conducting experiments on the continuous self-supervised learning problem. In this setup, models should learn from a continuous (infinite) non-IID data stream that follows a non-stationary distribution of visual concepts. The goal is to learn representations that are robust, adaptive yet not forgetful of concepts seen in the past. We show that a direct application of current methods to continuous SSL is 1) inefficient both computationally and in the amount of data required, 2) leads to inferior representations due to temporal correlations (non-IID data) in the streaming sources and 3) exhibits signs of catastrophic forgetting when trained on sources with non-stationary data distributions. We study the use of replay buffers to alleviate the issues of inefficiency and temporal correlations, and enhance them by actively maintaining the least redundant samples in the buffer. We show that minimum redundancy (MinRed) buffers allow us to learn effective representations even in the most challenging streaming scenarios (e.g., sequential frames obtained from a single embodied agent), and alleviates the problem of catastrophic forgetting.