In high-energy heavy ion collisions, quarks and gluons are released from the colliding nucleus to form a new state of nuclear matter called deconfined quark gluon plasma (QGP). To study the transition from normal nuclear matter or hadron resonance gas to QGP, non-perturbative quantum chromodynamics (QCD) must be solved on supercomputers using the lattice numerical method (lattice Quantum Chromodynamics, lattice QCD). However, lattice QCD only works for zero and small baryon chemical potential regions that can be described by the Taylor expansion and provides the nuclear equation of state (EoS) and QCD transition in these regions. For large baryon chemical potential regions that cannot be described by the Taylor expansion, lattice QCD fails to provide the nuclear EoS and QCD transition owing to the famous sign problem. Machine learning helps to study the nuclear EoS and QCD phase transition. First, machine learning can determine the nuclear EoS and QCD transition using the momentum distribution of final state hadrons in heavy-ion collisions, with data from both heavy-ion collision experiments and relativistic hydrodynamic simulations. Second, it can contribute to the direct solution of the sign problem in lattice QCD. The present paper reviews the applications of machine learning to the study of the QCD phase transition in heavy-ion collisions. This study (1) introduces nuclear EoS and QCD transition as well as the difficulty of the lattice QCD method, (2) analyzes the nuclear EoS using Bayesian analysis, (3) identifies the nuclear EoS and QCD phase transition using different types of deep neural networks (e.g., convolutional neural network, point cloud network, and many-event averaging), (4) searches for critical self-similarity using a dynamical edge convolution-based graph neural network, (5) learns the quasi-particle mass using a physically informed network and auto-differentiation, (6) discards unphysical regions in the nuclear EoS with a critical endpoint using active learning, (7) discusses unsupervised learning for the nuclear liquid-gas phase transition, (8) determines the nuclear symmetry energy in heavy-ion collisions, (9) investigates Mach cones using deep learning assisted jet tomography, and (10) accelerates the sampling of lattice QCD configurations using a physically constrained neural network while solving the sign problem in lattice QCD using deep learning.