  Breakthroughs in machine learning in the last decade have led to `digital
intelligence', i.e. machine learning models capable of learning from vast
amounts of labeled data to perform several digital tasks such as speech
recognition, face recognition, machine translation and so on. The goal of this
thesis is to make progress towards designing algorithms capable of `physical
intelligence', i.e. building intelligent autonomous navigation agents capable
of learning to perform complex navigation tasks in the physical world involving
visual perception, natural language understanding, reasoning, planning, and
sequential decision making. Despite several advances in classical navigation
methods in the last few decades, current navigation agents struggle at
long-term semantic navigation tasks. In the first part of the thesis, we
discuss our work on short-term navigation using end-to-end reinforcement
learning to tackle challenges such as obstacle avoidance, semantic perception,
language grounding, and reasoning. In the second part, we present a new class
of navigation methods based on modular learning and structured explicit map
representations, which leverage the strengths of both classical and end-to-end
learning methods, to tackle long-term navigation tasks. We show that these
methods are able to effectively tackle challenges such as localization,
mapping, long-term planning, exploration and learning semantic priors. These
modular learning methods are capable of long-term spatial and semantic
understanding and achieve state-of-the-art results on various navigation tasks.
