In modern Machine Learning, model training is an iterative, experimental process that can consume enormous computation resources and developer time. To aid in that process, experienced model developers log and visualize program variables during training runs. Exhaustive logging of all variables is infeasible, so developers are left to choose between slowing down training via extensive conservative logging, or letting training run fast via minimalist optimistic logging that may omit key information. As a compromise, optimistic logging can be accompanied by program checkpoints; this allows developers to add log statements post-hoc, and "replay" desired log statements from checkpoint---a process we refer to as hindsight logging. Unfortunately, hindsight logging raises tricky problems in data management and software engineering. Done poorly, hindsight logging can waste resources and generate technical debt embodied in multiple variants of training code. In this paper, we present methodologies for efficient and effective logging practices for model training, with a focus on techniques for hindsight logging. Our goal is for experienced model developers to learn and adopt these practices. To make this easier, we provide an open-source suite of tools for Fast Low-Overhead Recovery (flor) that embodies our design across three tasks: (i) efficient background logging in Python, (ii) adaptive periodic checkpointing, and (iii) an instrumentation library that codifies hindsight logging for efficient and automatic record-replay of model-training. Model developers can use each flor tool separately as they see fit, or they can use flor in hands-free mode, entrusting it to instrument their code end-to-end for efficient record-replay. Our solutions leverage techniques from physiological transaction logs and recovery in database systems. Evaluations on modern ML benchmarks demonstrate that flor can produce fast checkpointing with small user-specifiable overheads (e.g. 7%), and still provide hindsight log replay times orders of magnitude faster than restarting training from scratch.