Grounding language to a navigating agent's observations can leverage pretrained multimodal foundation models to match perceptions to object or event descriptions. However, previous approaches remain disconnected from environment mapping, lack the spatial precision of geometric maps, or neglect additional modality information beyond vision. To address this, we propose multimodal spatial language maps as a spatial map representation that fuses pretrained multimodal features with a 3D reconstruction of the environment. We build these maps autonomously using standard exploration. We present two instances of our maps, which are visual-language maps (VLMaps) and their extension to audio-visual-language maps (AVLMaps) obtained by adding audio information. When combined with large language models (LLMs), VLMaps can (i) translate natural language commands into open-vocabulary spatial goals (e.g., "in between the sofa and TV") directly localized in the map, and (ii) be shared across different robot embodiments to generate tailored obstacle maps on demand. Building upon the capabilities above, AVLMaps extend VLMaps by introducing a unified 3D spatial representation integrating audio, visual, and language cues through the fusion of features from pretrained multimodal foundation models. This enables robots to ground multimodal goal queries (e.g., text, images, or audio snippets) to spatial locations for navigation. Additionally, the incorporation of diverse sensory inputs significantly enhances goal disambiguation in ambiguous environments. Experiments in simulation and real-world settings demonstrate that our multimodal spatial language maps enable zero-shot spatial and multimodal goal navigation and improve recall by 50% in ambiguous scenarios. These capabilities extend to mobile robots and tabletop manipulators, supporting navigation and interaction guided by visual, audio, and spatial cues.