Optical frequency combs have revolutionized spectral measurement technologies, such as dual-comb spectrometers, for fast and accurate spectroscopic measurements over broad spectral ranges. Moreover, chip-scale frequency combs based on microresonators are revolutionizing laser spectroscopy due to their compact size, low cost, and low power consumption, which offer a promising solution for integrated optical sensing applications by replacing costly bulk optical sensing components. Developing new attractive photonic materials for integrated microcomb is critical to realizing chip-based microcombs with high efficiency, broad bandwidth, and low pumping power. In this tutorial, we present novel chalcogenide chip-based microcombs for broadband laser spectroscopy. The integrated chalcogenide microresonators on silicon wafers are achieved using a home-developed chalcogenide glass (Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">25</sub> Sb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">65</sub> ) with ultra-wide transmittance window, high Kerr nonlinearity, and low thermo-optic coefficient. Two fabrication processes of high quality-factor integrated chalcogenide microresonators with different core-cladding structures operating in the telecom and mid-infrared (MIR) regions, respectively, are introduced. Combined high nonlinearity with lithographically controlled flexible dispersion engineering of the chalcogenide microresonators, we have realized the versatile Kerr microcombs generation and physical mechanism, including bright soliton microcomb, dark-pulse microcomb, Raman-Kerr microcomb, broadband Kerr microcomb and the future opportunity of the MIR Kerr comb. In addition, we review the most potent examples of dual-comb spectroscopy applications for molecular characterization and laser ranging with ultra-high sensitivity and high accuracy and discuss the challenges of realizing MIR microcombs with high performance and ultracompact footprint for laser spectroscopy.