Accurate　traffic　congestion　estimation　and　prediction　are　critical　building　blocks　for　smart　trip　planning　and　rerouting　decisions　in　transportation　systems.　Over　the　decades,　there　have　been　many　studies　focusing　on　traffic　congestion　estimation　and　prediction　with　different　statistical　approaches　(e.g.,　Markov　chain)　and　machine　learning　models　(e.g.,　clustering,　Bayesian　networks,　and　artificial　neural　networks).　However,　there　is　a　lack　of　a　unified　framework　to　address　the　mechanisms　of　different　models　and　integrate　the　advantages　of　different　methods　through　combinations.　This　paper　introduces　the　FD-Markov-LSTM　model,　a　hybrid　interpretable　approach　that　combines　the　fundamental　diagram　(FD),　Markov　chain,　and　long　short-term　memory　(LSTM).　The　aim　is　to　estimate　and　predict　traffic　states　by　integrating　statistical　data　in　both　congested　and　uncongested　scenarios.　The　FD-Markov-LSTM　model　leverages　the　FD　to　identify　hierarchical　traffic　states　and　utilizes　the　Markov　process　to　capture　the　probabilistic　transitions　between　these　states.　We　employ　the　LSTM　model　to　further　capture　the　residual　time　series　produced　by　the　Markov　chain　model　(assuming　a　memoryless　property)　to　enhance　the　estimation　and　prediction　performance.　The　proposed　model＇s　accuracy　in　estimating　and　predicting　traffic　flow　is　evaluated　using　empirical　data　from　three　case　studies　conducted　in　Beijing　and　Los　Angeles.　The　results　highlight　a　significant　improvement　in　accuracy　compared　to　classical　benchmark　models　such　as　the　Markov　model,　ARIMA　model,　k-Nearest　Neighbor　model,　Random　Forest　model,　and　LSTM.　Specifically,　the　FD-Markov-LSTM　model　achieves　reductions　of　over　39%　in　mean　absolute　error,　35%　in　root　mean　squared　error,　and　7.4%　in　mean　absolute　percentage　error.　These　results　clearly　demonstrate　that　the　FD-Markov-LSTM　model　outperforms　the　benchmark　models,　enabling　more　precise　predictions　of　traffic　flow.　©　2023　The　Author(s)