Large Language Models excel at reasoning and generation but their autoregressive, token-by-token inference makes them unnecessarily slow, expensive, and poorly calibrated for the many routine decisions (routing, gating, scoring, classification) that modern AI systems require at sub-second latency. A growing class of models addresses this gap: System 1 decision models, architectures that map an input directly to a typed, structured decision in a single forward pass. This guide provides a comprehensive, practitioner-oriented treatment of the field. We propose a five-family taxonomy covering encoder-based classifiers, reward models, non-autoregressive decision engines, contrastive decision models, and extraction models, and we provide in-depth coverage of each family's architecture, training methodology, and deployment trade-offs. A central theme is calibration: we develop the theory of proper scoring rules, analyze Reinforcement Learning for Calibrated Decisions (RLCD), and examine recently discovered phenomena including IIA violations, ordinal-scale bias, and few-shot recalibration under distribution shift. On the integration side, we describe how System 1 models serve as decision infrastructure within agentic workflows and System 1 + System 2 cascades that route between fast and slow models based on calibrated confidence. The guide covers 18 application domains, maps the rapidly growing open-source ecosystem (over 70 model reproductions in weeks), provides runnable code throughout, and includes a practitioner's checklist, an open-source model zoo, and 22 self-assessment questions with detailed answers. Spanning 190 references, it is intended as a unified entry point for researchers and engineers working at the intersection of fast decision-making, calibration, and production AI systems.

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