Decomposition has been the mainstream approach in classic mathematical programming for multi-objective optimization and multi-criterion decision-making. However, it was not properly studied in the context of evolutionary multi-objective optimization (EMO) until the development of multi-objective evolutionary algorithm based on decomposition (MOEA/D). In this two-part survey series, we use MOEA/D as the representative of decomposition-based EMO to review the up-to-date development in this area, and systematically and comprehensively analyze its research landscape. In the first part, we present a comprehensive survey of the development of MOEA/D from its origin to the current state-of-the-art approaches. In order to be self-contained, we start with a step-by-step tutorial that aims to help a novice quickly get onto the working mechanism of MOEA/D. Then, selected major developments of MOEA/D are reviewed according to its core design components including weight vector settings, subproblem formulations, selection mechanisms and reproduction operators. Besides, we also overview some selected advanced topics for constraint handling, optimization in dynamic and uncertain environments, computationally expensive objective functions, and preference incorporation. In the final part, we shed some light on emerging directions for future developments.