Image colorization aims to add color information to a grayscale image in a realistic way. Recent methods mostly rely on deep learning strategies. While learning to automatically colorize an image, one can define well-suited objective functions related to the desired color output. Some of them are based on a specific type of error between the predicted image and ground truth one, while other losses rely on the comparison of perceptual properties. But, is the choice of the objective function that crucial, i.e., does it play an important role in the results? In this chapter, we aim to answer this question by analyzing the impact of the loss function on the estimated colorization results. To that goal, we review the different losses and evaluation metrics that are used in the literature. We then train a baseline network with several of the reviewed objective functions, classic L1 and L2 losses, as well as more complex combinations such as Wasserstein GAN and VGG-based LPIPS loss. Quantitative results show that the models trained with VGG-based LPIPS provide overall slightly better results for most evaluation metrics. Qualitative results exhibit more vivid colors when with Wasserstein GAN plus the L2 loss or again with the VGG-based LPIPS. Finally, the convenience of quantitative user studies is also discussed to overcome the difficulty of properly assessing on colorized images, notably for the case of old archive photographs where no ground truth is available.