###### Abstract  
Silicon photonics is a low-cost and versatile platform for various applications. For design of silicon photonic devices, the light-material interaction within its complex subwavelength geometry is difficult to investigate analytically and therefore numerical simulations are majorly adopted. To make the design process more time-efficient and to improve the device performance to its physical limits, various methods have been proposed over the past few years to manipulate the geometries of silicon platform for specific applications. In this review paper, we summarize the design methodologies for silicon photonics including iterative optimization algorithms and deep neural networks. In case of iterative optimization methods, we discuss them in different scenarios in the sequence of increased degrees of freedom: empirical structure, QR-code like structure and irregular structure. We also review inverse design approaches assisted by deep neural networks, which generate multiple devices with similar structure much faster than iterative optimization methods and are thus suitable in situations where piles of optical components are needed. Finally, the applications of inverse design methodology in optical neural networks are also discussed. This review intends to provide the readers with the suggestion for the most suitable design methodology for a specific scenario. silicon photonics; inverse design; deep neural networks; optical neural networks 22 March 2021 2021 14 April 2021 23 April 2021 23 April 2021 23 April 2021 23 April 2021 23 23 April 2021 23 2 Iterative optimization algorithms can optimize device geometric parameters for targeted optical performance. They have been widely researched recently due to their time-efficiency and satisfactory optimization results. For devices with regular structure, key geometry parameters, which suggest the degrees of freedom (DOF) during design, are abstracted and tuned for targeted optical performance. For devices with one or two DOF, the optimal optical performance can be found by sweeping all the possible solutions. However, the sweeping process would be extremely laborious and require large time budget for higher DOF, as EM simulations are time-consuming. The relationships between geometry parameters and optical performance are quite similar to mathematical non-deterministic polynomial hard (NP-hard) problems [13] which are difficult to define by explicit function. Inspired by iterative gradient-free algorithms such as genetic algorithm (GA), particle swarm optimization (PSO) and direct binary search (DBS) for solving NP-hard problems, lots of regular silicon photonic devices are optimized in these ways [14]. Apart from gradient-free algorithms, gradient-based algorithms like topology optimization (TO) for devices with irregular structure have also been investigated for inverse design recently [15]. Instead of abstracting key parameters that describes device geometry, TO takes the whole design space as a bitmap, where all the pixels are iteratively updated towards the direction of gradient descent until the gradients are small enough. In this way, complex geometric pattern could be quickly generated for a targeted optical performance. The iterative optimization algorithms discussed above could optimize only one device for one-round optimization and the whole optimization process has to be repeated again when the optical response target varies a little. This is extremely laborious when many similar devices are needed with slightly difference target response, such as power splitters with different splitting ratios or grating couplers (GCs) working at different wavelength bands [16]. Fortunately, DNN, an unprecedented tool capable of building a bridge between data features and data labels, has also found its way to assist the design of silicon photonic devices [6]. Based on the mapping direction between geometric parameters and optical response, DNNs are trained as forward models and inverse models.