## 1 Introduction
Besides the two mature technologies of Ti:Sapphire and fiber lasers, diode-pumped solid-state lasers (DPSSLs) have proved during the last years to constitute a promising alternative for the realization of frequency combs with state-of-the-art performance. DPSSLs combine several distinct advantages of the two aforementioned comb technologies. Like Ti:Sapphire lasers, they can emit a high average power directly from the oscillator, without external amplification. They also have low cavity losses (thus a high Q-factor) that lead to low intrinsic noise. This generally results in a lower noise of the free-running CEO beat that makes its tight locking to an external frequency reference less demanding in terms of feedback bandwidth. Finally, operation at high repetition rates is much less challenging than for fiber lasers as very compact cavities can be built. As a result, gigahertz or multi-gigahertz repetition rates can be achieved [17, 18, 19, 20, 21], which is highly attractive for applications in microwave photonics [22] or for the calibration of astronomical spectrographs [23]. Like fiber lasers, DPSSLs are directly pumped by laser diodes, which circumvents several disadvantages associated with the complexity, high cost and inefficient pumping of Ti:Sapphire combs. Pump diodes are very compact, efficient and low-cost, which makes DPSSLs very reliable and robust laser sources. Furthermore, pump diodes can be directly modulated via their injection current with a high bandwidth, which enables simple control or stabilization of _f_/_cEO via the pump current. This is the most common method to CEO-stabilize fiber laser frequency combs using the self-referencing _f_-to-_2\(f\) interferometry method [24]. This method is applicable in a similar way in DPSSLs and constitutes the most common means to CEO-stabilize this type of femtosecond lasers [21, 25, 26, 27, 28, 29, 30, 31]. In this review article, we present the current status of CEO-stabilized DPSSLs including some of our own achievements as well as works from other groups worldwide. We will restrict our review to DPSSL systems that have been CEO-stabilized or which are self-referenceable (_i.e._, for which a CEO beat has been detected by _f_-to-_2\(f\) interferometry, but whose stabilization has not yet been realized), as the focus here is in their operation as frequency combs. An alternative scheme to stabilize the comb offset frequency consists of locking one comb mode to an optical frequency standard, e.g., a continuous wave laser referenced to some molecular or atomic transition. This is for instance a natural approach in Kerr-combs generated by parametric frequency conversion in continuously-pumped whispering gallery mode micro-resonators [32]. As the pump frequency coincides in this case with one line of the comb spectrum, it directly controls the offset frequency [33]. Such a scheme that circumvents the need for a coherent octave-spanning spectrum has also been applied in a few cases with fiber modelocked lasers [34, 35], but we are not aware of any implementation with a DPSSL comb. Furthermore, this approach generally leads to less accurate comb frequencies. Therefore, phase-stabilization of _f_/_cEO to a stable radio-frequency (RF) signal such as provided by a GPS-disciplined atomic clock using _f_-to-_2\(f\) interferometry leads to an absolute frequency grid that is required in many practical applications. For all these reasons, this review addresses only DPSSL combs that make use of _f_-to-_2\(f\) interferometry. We will consider both DPSSLs made of a bulk gain material and thin disk lasers (TDLs) that offer high power scaling capabilities. TDLs demonstrated record high multi-100 W average power [36] that makes them very attractive for high field physics experiments such as high-harmonic generation (HHG) [37].