Photoacoustic imaging, an emerging modality that seamlessly combines advantages of optical absorption contrast and ultrasound resolution, holds great promise for noninvasive imaging of biological tissues. Its applications span across diverse fields, such as dermatology, oncology, cardiology, and neurology. However, achieving accurate image reconstruction and physiological parameters quantification from raw photoacoustic signals presents a significant challenge. This challenge primarily arises from the inherent heterogeneity of tissues, encompassing variations in optical fluence and acoustic properties. In addition, incomplete information acquired from a limited view also leads to artifacts, image distortions, and reduced spatial resolution. Furthermore, robust spectral unmixing approach is another key step to restore the initial biochemical components' distribution with complex or unknown background absorption. To overcome these hurdles, researchers have proposed numerous state-of-the-art techniques, aiming to improve the accuracy and reliability of quantitative photoacoustic imaging (qPAI) in heterogeneous tissue. This review aims to comprehensively overview recent developments over the past decade, for addressing four main challenges frequently encountered in qPAI: limited-view reconstruction, acoustic heterogeneity, optical fluence fluctuations, and robust spectral unmixing, which serves as a reference for readers seeking to understand the specific challenges and corresponding solutions in this field.