In the past few decades, considerable scientific strides have been made in the subject of drug analysis in human biological samples. However, the risk caused by incorrect drug plasma levels in patients still remains an important concern. This review paper attempts to investigate the advances made over the last ten years in common sample preparation techniques (SPT) for biological samples based on solid sorbents, including solid-phase extraction (SPE) and solid-phase micro-extraction (SPME), and in particular in the field of molecularly imprinted polymers (MIPs), including non-stimuli-responsive and stimuli-responsive adsorbents. This class of materials is known as ‘smart adsorbents’, exhibiting tailored responses to various stimuli such as magnetic fields, pH, temperature, and light. Details are provided on how these advanced SPT are changing the landscape of modern drug analysis in their coupling with liquid chromatography-mass spectrometry (LC-MS) analytical techniques, a general term that includes high-performance liquid chromatography (HPLC) and ultra-high performance liquid chromatography (UHPLC), as well as any variation of MS, such as tandem (MS/MS), multiple-stage (MSn), and high-resolution (HRMS) mass spectrometry. Some notes are also provided on coupling with less-performing techniques, such as high-performance liquid chromatography with ultraviolet (HPLC-UV) and diode array detection (HPLC-DAD) detection. Finally, we provide a general review of the difficulties and benefits of the proposed approaches and the future prospects of this research area.