The discrepancy between the local measurement of the Hubble constant using the distance ladder and the determination from the cosmic microwave background (CMB) presents a significant challenge to the standard cosmological model Lambda-CDM. To address this tension, independent measurements of the Hubble constant are crucial. Here, we present two distinct approaches to determine the Hubble constant without relying on the cosmic distance ladder.
Firstly, we introduce the adH0cc program, which aims to measure the local Hubble constant using Type II supernovae. By modelling the simple hydrogen-rich material of these supernovae with modern radiative-transfer techniques, we can accurately determine their luminosity distances. Leveraging a dedicated dataset of over 20 Type II supernovae, combined with advanced spectral emulation and Bayesian statistical methods, we anticipate to achieve a precision better than 3% in our Hubble-constant determination. 
Secondly, we discuss the efforts of the HOLISMOKES team to utilise strong gravitational lensing as a method to measure the Hubble constant. By analysing time delays between multiple images in strongly lensed supernovae, we can determine the "time-delay distance," which is inversely proportional to the Hubble constant. Although limited by the scarcity of lensed supernovae and the depth of current sky surveys, upcoming surveys such as LSST and Euclid hold the promise of significantly expanding the sample size. This expansion could establish lensed-supernova time delays as a competitive cosmological probe. 
Both approaches offer critical and independent tests of the Hubble tension.