We present a new framework for semantic segmentation without annotations via clustering. Off-the-shelf clustering methods are limited to curated, single-label, and object-centric images yet real-world data are dominantly uncurated, multi-label, and scene-centric. We extend clustering from images to pixels and assign separate cluster membership to different instances within each image. However, solely relying on pixel-wise feature similarity fails to learn high-level semantic concepts and overfits to low-level visual cues. We propose a method to incorporate geometric consistency as an inductive bias to learn invariance and equivariance for photometric and geometric variations. With our novel learning objective, our framework can learn high-level semantic concepts. Our method, PiCIE (Pixel-level feature Clustering using Invariance and Equivariance), is the first method capable of segmenting both things and stuff categories without any hyperparameter tuning or task-specific pre-processing. Our method largely outperforms existing baselines on COCO and Cityscapes with +17.5 Acc. and +4.5 mIoU. We show that PiCIE gives a better initialization for standard supervised training. The code is available at https://github.com/janghyuncho/PiCIE.